Dr D Madhusudhana Rao | Acharya Nagarjuna University (original) (raw)
Papers by Dr D Madhusudhana Rao
International Journal on Future Revolution in Computer Science & Communication Engineering, Oct 31, 2017
In this paper the term, left(lateral, right and two sided) PO-ternary ideal, maximal left(lateral... more In this paper the term, left(lateral, right and two sided) PO-ternary ideal, maximal left(lateral, right and two sided) PO-ternary ideal, left (lateral, right and two sided) PO-ternary ideal of T generated by a set A, principal left (lateral, right and two sided) PO-ternary ideal generated by an element a left (lateral, right and two sided) simple PO-ternary semiring are introduced. It is proved that (1) the non-empty intersection of any two left (lateral, right and two sided) PO-ternary ideals of a PO-ternary semiring T is a left (lateral, right and two sided) PO-ternary ideal of T. (2) non-empty intersection of any family of left (lateral, right and two sided) PO-ternary ideals of a POternary semiring T is a left(lateral, right and two sided) PO-ternary ideal of T. (3) the union of any left PO-ternary ideals of a PO-ternary semiring T is a left PO-ternary ideal of T. (4) the union of any family of left(lateral, right and two sided) PO-ternary ideals of a PO-ternary semiring T is a...
He is pursuing Ph.D. under the guidance of Dr.D.MadhusudanaRao in AcharyaNagarjuna University. He... more He is pursuing Ph.D. under the guidance of Dr.D.MadhusudanaRao in AcharyaNagarjuna University. He published more than 7 research papers in popular international Journals to his credit. His area of interests are ternary semirings, ordered ternary semirings, semirings. Presently he is working on Partially Ordered Ternary semirings. 3 G. SrinivasaRao: He is working as an Assistant Professor in the Department of Applied Sciences & Humanities, Tirumala Engineering College. He completed his M.Phil. inMadhuraiKamaraj University. He is pursuing Ph.D. under the guidance of Dr.D.MadhusudanaRao in AcharyaNagarjuna University. He published more than 20 research papers in popular international Journals to his credit. His area of interests are ternary semirings, ordered ternary semirings, semirings and topology. Presentlyhe is working on Ternary semirings.
semigroup ’ for an ideal A of a ternary semigroup are introduced. If A is an ideal of a ternary s... more semigroup ’ for an ideal A of a ternary semigroup are introduced. If A is an ideal of a ternary semigroup T then it is proved that (1) A � N A) � N ( A) � N ( ) (2) N0(A) = A2, N1(A) is a semiprime ideal of T
Malaya Journal of Matematik, 2021
The notation of prime bi-interior ideal, semi prime bi-interior ideal, irreducible bi-interior id... more The notation of prime bi-interior ideal, semi prime bi-interior ideal, irreducible bi-interior ideal and strongly prime bi-interior ideal of TG-Semi ring (ternary gamma semi-ring) are introduced. We study properties of these ideals and relations between them and also characterize regular TG-Semi-ring and TG-Semi-ring using prime bi-interior ideals, irreducible and strongly irreducible bi-interior ideals in this article. Keywords TGS, bi-interior ideal, prime ideals, prime bi-interior ideal, strong prime bi-interior ideal, semi prime bi-interior ideal and irreducible and strongly irreducible bi-interior ideals.
In this paper the terms P-primary, primary decomposition of a ડ -ideal, reduced primary decomposi... more In this paper the terms P-primary, primary decomposition of a ડ -ideal, reduced primary decomposition of a ડ -ideal in a ડ -semigroup S are introduced. If A1, A2, …An are P-primary ડ ideals in a ડ -semigroup S, then it is proved that 1 n
This paper is divided into four sections, in section 1, introduction of the paper. In section 2, ... more This paper is divided into four sections, in section 1, introduction of the paper. In section 2, we provided some preliminaries which are useful for further development of the paper. In section 3, we were introduced bi-ternary Γ-ideals, strongly bi-ternary Γ-ideals and semiprime bi-ternary Γ- ideals in ternary Γ-semirings. It is proved that (1) Every strongly prime bi-ternary Γ-ideal of a ternary Γ-semiring T is a prime bi-ternary Γ-ideal of T. (2) Every prime bi-ternary Γ-ideal of a ternary Γ-semiring T is a semiprime bi-ternary Γ-ideal of T. In section 4, the terms irreducible and strongly irreducible bi-ternary Γ-ideals in ternary Γ-semiring. It is proved that if B be a biternary Γ-ideal of a ternary Γ-semiring T and a ∈ T such that a∉ B. Then there exists an irreducible bi-ternary Γ-ideal I of T such that B ⊆ I and a ∉ I.
Our aim in this paper is to develop a body of results on the minimality and maximality of ordered... more Our aim in this paper is to develop a body of results on the minimality and maximality of ordered quasi-Γ-ideals in ordered ternary Γ-semirings, that can be used like the more classical results on unordered structures. Index Terms — ordered ternary Γ-semiring, ordered quasi-Γ-ideal, minimality and maximality.
1.Introduction Anjaneyulu [1] made a study on primary ideals in semigroups. Later Anjanetulu [2] ... more 1.Introduction Anjaneyulu [1] made a study on primary ideals in semigroups. Later Anjanetulu [2] made a study on semigroups in which prime ideals are maximal. The study of ternary algebraic systems had been made by Lehmer [5], but earlier ternary structure was studied by Kerner [4] who give the idea of n-ary algebras. Aiyared Iampan [3] characteriae the relationship between the 0-minimal and maximal lateral ideals and the lateral 0-simple ternary semigroups. Los [6] studied some properties of ternary semigroup and proved that every ternary semigroup can be embedded in a semigroup. Shabir and Bashir [8] launched prime ideals in ternary semigroups. Sarala. Y, Anjaneyulu. A and Madhusudhana Rao. D [7] studied about globally idempotent ternary semigroups and proved that every maximal ideal of a globally idempotent ternary semigroup T is a prime ideal of T. In this paper we characterize quasi commutative ternary semigroup, semipseudo symmetric ternary semigroup and quasi commutative tern...
This paper is divided into four sections, in section 1, introduction of the paper. In section 2, ... more This paper is divided into four sections, in section 1, introduction of the paper. In section 2, we provided some preliminaries which are useful for further development of the paper. In section 3, we were introduced bi-ternary Γ-ideals, strongly bi-ternary Γ-ideals and semiprime bi-ternary Γ- ideals in ternary Γ-semirings. It is proved that (1) Every strongly prime bi-ternary Γ-ideal of a ternary Γ-semiring T is a prime bi-ternary Γ-ideal of T. (2) Every prime bi-ternary Γ-ideal of a ternary Γ-semiring T is a semiprime bi-ternary Γ-ideal of T. In section 4, the terms irreducible and strongly irreducible bi-ternary Γ-ideals in ternary Γ-semiring. It is proved that if B be a biternary Γ-ideal of a ternary Γ-semiring T and a ∈ T such that a∉ B. Then there exists an irreducible bi-ternary Γ-ideal I of T such that B ⊆ I and a ∉ I.
This paper is divided into four sections, in section 1, introduction of the paper. In section 2, ... more This paper is divided into four sections, in section 1, introduction of the paper. In section 2, we provided some preliminaries which are useful for further development of the paper. In section 3, we were introduced bi-ternary Γ-ideals, strongly bi-ternary Γ-ideals and semiprime bi-ternary Γ-ideals in ternary Γ-semirings. It is proved that (1) Every strongly prime bi-ternary Γ-ideal of a ternary Γ-semiring T is a prime bi-ternary Γ-ideal of T. (2 ) Every prime bi-ternary Γ-ideal of a ternary Γ-semiring T is a semiprime bi-ternary Γ-ideal of T. In section 4, the terms irreducible and strongly irreducible bi-ternary Γ-ideals in ternary Γ-semiring. It is proved that if B be a bi-ternary Γ-ideal of a ternary Γ-semiring T and a ∈ T such that a ∉ B. Then there exists an irreducible bi-ternary Γ-ideal I of T such that B ⊆ I and a ∉ I. Further it is proved that in a ternary
In this paper we introduce the terms ternary Γ-semiring, commutative ternary Γ-semiring, left ter... more In this paper we introduce the terms ternary Γ-semiring, commutative ternary Γ-semiring, left ternary Γ-ideal, lateral ternary Γ-ideal, right ternary Γ-ideal, ternary Γ-ideal, prime lateral ternary Γ-ideal, semiprime ternary Γ-ideal, irreducible ternary Γ-ideal and strongly irreducible ternary Γ- ideal and characterize the ternary Γ-ideals and proved many results. Mathematics Subject Classification: 20G07, 20M10, 20M12, 20M14, 20N10.
In this paper the terms completely prime ideal, prime ideal, m-system. globally idempotent , semi... more In this paper the terms completely prime ideal, prime ideal, m-system. globally idempotent , semi simple elements of a ternary semigroup are Introduced. It is proved that an ideal A of a ternary semigroup T is completely prime if and only if T\A is either sub semigroup of T or empty. It is proved that if T is a globally idempotent ternary semigroup then every maximal ideal of T is a prime ideal of T. In this paper the terms completely semiprime ideal, semiprime ideal, n-system, d-system and i-system are introduced. It is proved that the non-empty intersection of any family of a completely prime ideal and prime ideal of a ternary semigroup T is a completely semiprime ideal of T. It is also proved that an ideal A of a ternary semigroup T is completely semiprime if and only if T\A is a d-system of T or empty. It is proved that if N is an n-system in a ternary semigroup T and aN, then there exist an m-system M in T such that aM and M N. The terms radical, complete radical of a terna...
international journal of chemical sciences, 2017
The paper introduces the concepts of β-insulator and strongly prime-semigroups. Several character... more The paper introduces the concepts of β-insulator and strongly prime-semigroups. Several characterizations of them are furnished.
In this paper a Γ -semigroup S with identity, if √A = M for some Γ -ideal of S, where M is the un... more In this paper a Γ -semigroup S with identity, if √A = M for some Γ -ideal of S, where M is the unique maximal Γ-ideal of S, then A is a primary Γ -ideal. It is proved that if S is a Γ semigroup with identity, then for any natural number n, (MΓ) n-1 M is primary Γ -ideal of S, where M is the unique maximal Γ-ideal of S. Further it is proved that in quasi commutative semigroup S, a Γ-ideal A of S is left primary iff A is right primary. It is proved that in semipseudo symmetric semiprimary Γ-semigroup, globally idempotent principal Γ-ideals form a chain under set inclusion. In a semisimple Γ-semigroup S it is proved that the conditions every ideal of S is prime, S is a primary Γ-semigroup, S is a left primary Γsemigroup, S is a right primary Γ-semigroup, S is a semiprimary Γ-semigroup, prime Γ-ideals of S form a chain, principal Γ-ideals of S form a chain, Γ-ideals of S form a chain are equivalent. Mathematical subject classification (2010) : 20M07; 20M11; 20M12.
T then it is proved that (1) ) ( ) ( ) ( 0 1 2 A N A N A N A (2) N0(A) = A2, N1(A) is a sem... more T then it is proved that (1) ) ( ) ( ) ( 0 1 2 A N A N A N A (2) N0(A) = A2, N1(A) is a semiprime ideal of T containing A, N2(A) = A4 are equivalent, where No(A) = The set of all A-potent elements in T, N1(A) = The largest ideal contained in No(A), N2(A) = The union of all A-potent ideals. If A is a semipseudo symmetric ideal of a ternary semigroup then it is proved that N0(A) = N1(A) = N2(A). It is also proved that if A is an ideal of a ternary semigroup such that N0(A) = A then A is a completely semiprime ideal. Further it is proved that if A is an ideal of ternary semigroup T then R(A), the divisor radical of A, is the union of all A-divisor ideals in T. In a N(A)ternary semigroup it is proved that R(A) = N1(A). If A is a semipseudo symmetric ideal of a ternary semigroup T then it is proved that S is an N(A)ternary semigroup iff R(A) = N0(A). It is also proved that if M is a maximal ideal of a ternary semigroup T containing a pseudo symmetric ideal A then M contains all A-p...
In this paper we study some interesting properties of regular ternary Γ-semigroups, completely re... more In this paper we study some interesting properties of regular ternary Γ-semigroups, completely regular ternary Γ-semigroups, intra-regular ternary Γ-semigroups and characterize them by using various ternary Γ-ideals of ternary Γ-semigroups. AMS Subject Classification: 20M17
Γsemigroup was introduced by Sen and Saha [11] as a generalization of semigroup. Anjaneyulu. A [1... more Γsemigroup was introduced by Sen and Saha [11] as a generalization of semigroup. Anjaneyulu. A [1], [2] and [3] initiated the study of pseudo symmetric ideals, radicals and semipseudo symmetric ideals in semigroups. Giri and wazalwar [7] intiated the study of prime radicals in semigroups. Madhusudhana Rao, Anjaneyulu and Gangadhara Rao [8], [9] initiated the study of pseudo symmetric Γ-ideals and prime radicals in Γ-semigroups. In this paper we introduce the notions of semipseudo symmetric Γ-ideals in Γ-semigroup and characterize the semipseudo symmetric Γ-ideals in Γ-semigroups.
The terms, ‘I-dominant’, ‘left I-divisor’, ‘right I-divisor’, ‘I-divisor’ elements, ‘M (I)-ternar... more The terms, ‘I-dominant’, ‘left I-divisor’, ‘right I-divisor’, ‘I-divisor’ elements, ‘M (I)-ternary Γ-semigroup’ for a ternary Γ-ideal I of a ternary Γ-semigroup are introduced and we characterized M (I)-ternary gamma semigroups.
International Journal on Future Revolution in Computer Science & Communication Engineering, Oct 31, 2017
In this paper the term, left(lateral, right and two sided) PO-ternary ideal, maximal left(lateral... more In this paper the term, left(lateral, right and two sided) PO-ternary ideal, maximal left(lateral, right and two sided) PO-ternary ideal, left (lateral, right and two sided) PO-ternary ideal of T generated by a set A, principal left (lateral, right and two sided) PO-ternary ideal generated by an element a left (lateral, right and two sided) simple PO-ternary semiring are introduced. It is proved that (1) the non-empty intersection of any two left (lateral, right and two sided) PO-ternary ideals of a PO-ternary semiring T is a left (lateral, right and two sided) PO-ternary ideal of T. (2) non-empty intersection of any family of left (lateral, right and two sided) PO-ternary ideals of a POternary semiring T is a left(lateral, right and two sided) PO-ternary ideal of T. (3) the union of any left PO-ternary ideals of a PO-ternary semiring T is a left PO-ternary ideal of T. (4) the union of any family of left(lateral, right and two sided) PO-ternary ideals of a PO-ternary semiring T is a...
He is pursuing Ph.D. under the guidance of Dr.D.MadhusudanaRao in AcharyaNagarjuna University. He... more He is pursuing Ph.D. under the guidance of Dr.D.MadhusudanaRao in AcharyaNagarjuna University. He published more than 7 research papers in popular international Journals to his credit. His area of interests are ternary semirings, ordered ternary semirings, semirings. Presently he is working on Partially Ordered Ternary semirings. 3 G. SrinivasaRao: He is working as an Assistant Professor in the Department of Applied Sciences & Humanities, Tirumala Engineering College. He completed his M.Phil. inMadhuraiKamaraj University. He is pursuing Ph.D. under the guidance of Dr.D.MadhusudanaRao in AcharyaNagarjuna University. He published more than 20 research papers in popular international Journals to his credit. His area of interests are ternary semirings, ordered ternary semirings, semirings and topology. Presentlyhe is working on Ternary semirings.
semigroup ’ for an ideal A of a ternary semigroup are introduced. If A is an ideal of a ternary s... more semigroup ’ for an ideal A of a ternary semigroup are introduced. If A is an ideal of a ternary semigroup T then it is proved that (1) A � N A) � N ( A) � N ( ) (2) N0(A) = A2, N1(A) is a semiprime ideal of T
Malaya Journal of Matematik, 2021
The notation of prime bi-interior ideal, semi prime bi-interior ideal, irreducible bi-interior id... more The notation of prime bi-interior ideal, semi prime bi-interior ideal, irreducible bi-interior ideal and strongly prime bi-interior ideal of TG-Semi ring (ternary gamma semi-ring) are introduced. We study properties of these ideals and relations between them and also characterize regular TG-Semi-ring and TG-Semi-ring using prime bi-interior ideals, irreducible and strongly irreducible bi-interior ideals in this article. Keywords TGS, bi-interior ideal, prime ideals, prime bi-interior ideal, strong prime bi-interior ideal, semi prime bi-interior ideal and irreducible and strongly irreducible bi-interior ideals.
In this paper the terms P-primary, primary decomposition of a ડ -ideal, reduced primary decomposi... more In this paper the terms P-primary, primary decomposition of a ડ -ideal, reduced primary decomposition of a ડ -ideal in a ડ -semigroup S are introduced. If A1, A2, …An are P-primary ડ ideals in a ડ -semigroup S, then it is proved that 1 n
This paper is divided into four sections, in section 1, introduction of the paper. In section 2, ... more This paper is divided into four sections, in section 1, introduction of the paper. In section 2, we provided some preliminaries which are useful for further development of the paper. In section 3, we were introduced bi-ternary Γ-ideals, strongly bi-ternary Γ-ideals and semiprime bi-ternary Γ- ideals in ternary Γ-semirings. It is proved that (1) Every strongly prime bi-ternary Γ-ideal of a ternary Γ-semiring T is a prime bi-ternary Γ-ideal of T. (2) Every prime bi-ternary Γ-ideal of a ternary Γ-semiring T is a semiprime bi-ternary Γ-ideal of T. In section 4, the terms irreducible and strongly irreducible bi-ternary Γ-ideals in ternary Γ-semiring. It is proved that if B be a biternary Γ-ideal of a ternary Γ-semiring T and a ∈ T such that a∉ B. Then there exists an irreducible bi-ternary Γ-ideal I of T such that B ⊆ I and a ∉ I.
Our aim in this paper is to develop a body of results on the minimality and maximality of ordered... more Our aim in this paper is to develop a body of results on the minimality and maximality of ordered quasi-Γ-ideals in ordered ternary Γ-semirings, that can be used like the more classical results on unordered structures. Index Terms — ordered ternary Γ-semiring, ordered quasi-Γ-ideal, minimality and maximality.
1.Introduction Anjaneyulu [1] made a study on primary ideals in semigroups. Later Anjanetulu [2] ... more 1.Introduction Anjaneyulu [1] made a study on primary ideals in semigroups. Later Anjanetulu [2] made a study on semigroups in which prime ideals are maximal. The study of ternary algebraic systems had been made by Lehmer [5], but earlier ternary structure was studied by Kerner [4] who give the idea of n-ary algebras. Aiyared Iampan [3] characteriae the relationship between the 0-minimal and maximal lateral ideals and the lateral 0-simple ternary semigroups. Los [6] studied some properties of ternary semigroup and proved that every ternary semigroup can be embedded in a semigroup. Shabir and Bashir [8] launched prime ideals in ternary semigroups. Sarala. Y, Anjaneyulu. A and Madhusudhana Rao. D [7] studied about globally idempotent ternary semigroups and proved that every maximal ideal of a globally idempotent ternary semigroup T is a prime ideal of T. In this paper we characterize quasi commutative ternary semigroup, semipseudo symmetric ternary semigroup and quasi commutative tern...
This paper is divided into four sections, in section 1, introduction of the paper. In section 2, ... more This paper is divided into four sections, in section 1, introduction of the paper. In section 2, we provided some preliminaries which are useful for further development of the paper. In section 3, we were introduced bi-ternary Γ-ideals, strongly bi-ternary Γ-ideals and semiprime bi-ternary Γ- ideals in ternary Γ-semirings. It is proved that (1) Every strongly prime bi-ternary Γ-ideal of a ternary Γ-semiring T is a prime bi-ternary Γ-ideal of T. (2) Every prime bi-ternary Γ-ideal of a ternary Γ-semiring T is a semiprime bi-ternary Γ-ideal of T. In section 4, the terms irreducible and strongly irreducible bi-ternary Γ-ideals in ternary Γ-semiring. It is proved that if B be a biternary Γ-ideal of a ternary Γ-semiring T and a ∈ T such that a∉ B. Then there exists an irreducible bi-ternary Γ-ideal I of T such that B ⊆ I and a ∉ I.
This paper is divided into four sections, in section 1, introduction of the paper. In section 2, ... more This paper is divided into four sections, in section 1, introduction of the paper. In section 2, we provided some preliminaries which are useful for further development of the paper. In section 3, we were introduced bi-ternary Γ-ideals, strongly bi-ternary Γ-ideals and semiprime bi-ternary Γ-ideals in ternary Γ-semirings. It is proved that (1) Every strongly prime bi-ternary Γ-ideal of a ternary Γ-semiring T is a prime bi-ternary Γ-ideal of T. (2 ) Every prime bi-ternary Γ-ideal of a ternary Γ-semiring T is a semiprime bi-ternary Γ-ideal of T. In section 4, the terms irreducible and strongly irreducible bi-ternary Γ-ideals in ternary Γ-semiring. It is proved that if B be a bi-ternary Γ-ideal of a ternary Γ-semiring T and a ∈ T such that a ∉ B. Then there exists an irreducible bi-ternary Γ-ideal I of T such that B ⊆ I and a ∉ I. Further it is proved that in a ternary
In this paper we introduce the terms ternary Γ-semiring, commutative ternary Γ-semiring, left ter... more In this paper we introduce the terms ternary Γ-semiring, commutative ternary Γ-semiring, left ternary Γ-ideal, lateral ternary Γ-ideal, right ternary Γ-ideal, ternary Γ-ideal, prime lateral ternary Γ-ideal, semiprime ternary Γ-ideal, irreducible ternary Γ-ideal and strongly irreducible ternary Γ- ideal and characterize the ternary Γ-ideals and proved many results. Mathematics Subject Classification: 20G07, 20M10, 20M12, 20M14, 20N10.
In this paper the terms completely prime ideal, prime ideal, m-system. globally idempotent , semi... more In this paper the terms completely prime ideal, prime ideal, m-system. globally idempotent , semi simple elements of a ternary semigroup are Introduced. It is proved that an ideal A of a ternary semigroup T is completely prime if and only if T\A is either sub semigroup of T or empty. It is proved that if T is a globally idempotent ternary semigroup then every maximal ideal of T is a prime ideal of T. In this paper the terms completely semiprime ideal, semiprime ideal, n-system, d-system and i-system are introduced. It is proved that the non-empty intersection of any family of a completely prime ideal and prime ideal of a ternary semigroup T is a completely semiprime ideal of T. It is also proved that an ideal A of a ternary semigroup T is completely semiprime if and only if T\A is a d-system of T or empty. It is proved that if N is an n-system in a ternary semigroup T and aN, then there exist an m-system M in T such that aM and M N. The terms radical, complete radical of a terna...
international journal of chemical sciences, 2017
The paper introduces the concepts of β-insulator and strongly prime-semigroups. Several character... more The paper introduces the concepts of β-insulator and strongly prime-semigroups. Several characterizations of them are furnished.
In this paper a Γ -semigroup S with identity, if √A = M for some Γ -ideal of S, where M is the un... more In this paper a Γ -semigroup S with identity, if √A = M for some Γ -ideal of S, where M is the unique maximal Γ-ideal of S, then A is a primary Γ -ideal. It is proved that if S is a Γ semigroup with identity, then for any natural number n, (MΓ) n-1 M is primary Γ -ideal of S, where M is the unique maximal Γ-ideal of S. Further it is proved that in quasi commutative semigroup S, a Γ-ideal A of S is left primary iff A is right primary. It is proved that in semipseudo symmetric semiprimary Γ-semigroup, globally idempotent principal Γ-ideals form a chain under set inclusion. In a semisimple Γ-semigroup S it is proved that the conditions every ideal of S is prime, S is a primary Γ-semigroup, S is a left primary Γsemigroup, S is a right primary Γ-semigroup, S is a semiprimary Γ-semigroup, prime Γ-ideals of S form a chain, principal Γ-ideals of S form a chain, Γ-ideals of S form a chain are equivalent. Mathematical subject classification (2010) : 20M07; 20M11; 20M12.
T then it is proved that (1) ) ( ) ( ) ( 0 1 2 A N A N A N A (2) N0(A) = A2, N1(A) is a sem... more T then it is proved that (1) ) ( ) ( ) ( 0 1 2 A N A N A N A (2) N0(A) = A2, N1(A) is a semiprime ideal of T containing A, N2(A) = A4 are equivalent, where No(A) = The set of all A-potent elements in T, N1(A) = The largest ideal contained in No(A), N2(A) = The union of all A-potent ideals. If A is a semipseudo symmetric ideal of a ternary semigroup then it is proved that N0(A) = N1(A) = N2(A). It is also proved that if A is an ideal of a ternary semigroup such that N0(A) = A then A is a completely semiprime ideal. Further it is proved that if A is an ideal of ternary semigroup T then R(A), the divisor radical of A, is the union of all A-divisor ideals in T. In a N(A)ternary semigroup it is proved that R(A) = N1(A). If A is a semipseudo symmetric ideal of a ternary semigroup T then it is proved that S is an N(A)ternary semigroup iff R(A) = N0(A). It is also proved that if M is a maximal ideal of a ternary semigroup T containing a pseudo symmetric ideal A then M contains all A-p...
In this paper we study some interesting properties of regular ternary Γ-semigroups, completely re... more In this paper we study some interesting properties of regular ternary Γ-semigroups, completely regular ternary Γ-semigroups, intra-regular ternary Γ-semigroups and characterize them by using various ternary Γ-ideals of ternary Γ-semigroups. AMS Subject Classification: 20M17
Γsemigroup was introduced by Sen and Saha [11] as a generalization of semigroup. Anjaneyulu. A [1... more Γsemigroup was introduced by Sen and Saha [11] as a generalization of semigroup. Anjaneyulu. A [1], [2] and [3] initiated the study of pseudo symmetric ideals, radicals and semipseudo symmetric ideals in semigroups. Giri and wazalwar [7] intiated the study of prime radicals in semigroups. Madhusudhana Rao, Anjaneyulu and Gangadhara Rao [8], [9] initiated the study of pseudo symmetric Γ-ideals and prime radicals in Γ-semigroups. In this paper we introduce the notions of semipseudo symmetric Γ-ideals in Γ-semigroup and characterize the semipseudo symmetric Γ-ideals in Γ-semigroups.
The terms, ‘I-dominant’, ‘left I-divisor’, ‘right I-divisor’, ‘I-divisor’ elements, ‘M (I)-ternar... more The terms, ‘I-dominant’, ‘left I-divisor’, ‘right I-divisor’, ‘I-divisor’ elements, ‘M (I)-ternary Γ-semigroup’ for a ternary Γ-ideal I of a ternary Γ-semigroup are introduced and we characterized M (I)-ternary gamma semigroups.