T-Systems in Ternary Semigroups (original) (raw)
T-Homomorphism of Semispaces in Ternary Semigroups
In this paper we introduce semispaces and characterize idempotents of rank 1 and exhibit a class of primitive idempotents of rank 1 in the ternary semigrooup of all T-homomorphisms on a semispace. We obtain a characterization of minimal (one sided) ideals in ternary semigroups of T-homomorphisms of a semispace containing all T-homomorphisms of rank 1 and obtain equivalent conditions for the ternary semigroup of Thomomorphisms on a semispace, to be a ternary group.
Relations on Ternary Semigroups
International Journal of Geometric Methods in Modern Physics, 2018
In this paper, we define certain equivalence relations called *-relations on ternary semigroups and we mention some properties of these relations. We study these relations in respect to Green’s relations in ternary semigroups and by bringing some examples, we show that while some propositions are correct for Green’s relations, they are not necessarily true for these relations. Then we investigate *-relations in certain ternary semigroups.
Special Types of Ternary Semigroups V . Jyothi
2014
The main goal of this paper is to initiate the notions of U-ternarysemigroup and V-ternary semigroup in the class of orbitary ternarysemigroups. We study prime ideals and maximal ideals in a Uternarysemigroup and characterize V-ternary semigroup. It is proved that if T is a globally idempotent ternarysemigroups with maximal ideal, then either T is a V-ternarysemigroup or T has a unique maximal ideal which is prime. Finally we proved that a ternarysemigroup T is a V-ternarysemigroup if and only if T has atleast one proper prime ideal and if { } is the family of all proper prime ideals, then < x > =T for x T\U or T is a simple ternarysemigroup.
A STUDY ON d-SYSTEM, m-SYSTEM AND n-SYSTEM IN TERNARY SEMIGROUPS
Qualitative In this paper the terms d-system, m-system, n-system, U-ternary semigroup are introduced. It is proved that an ideal A of a ternary semigroup T is a prime ideal of T if and only if T\A is an m-system of T or empty. It is 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 every msystem in a ternary semigroup T is an n-system. Further it is proved that an ideal Q of a ternary semigroup T is a semiprime ideal if and only if T\Q is an n-system of T (or) empty. It is proved that if N is an n-system in a ternary semigroup T and a N, then there exist an m-system M in T such that a M and M N. It is proved that a ternary semigroup T is U-ternary semigroup if
Chained Commutative Ternary Semigroups
In this paper, the terms chained ternary semigroup, cancellable clement , cancellative ternary semigroup, A-regular element, π-regular element, πinvertible element, noetherian ternary semigroup are introduced. It is proved that in a commutative chained ternary semigroup T, i) if P is a prime ideal of T and x ∉ P then n n1
J . Semigroup Theory Appl . 2013 , 2013 : 6 ISSN 2051-2937 GREEN ’ S RELATIONS ON TERNARY SEMIGROUPS
2013
Algebraic structures play a prominent role in mathematics with wide ranging applications in many disciplines such as theoretical physics, computer sciences, control engineering, information sciences, coding theory, topological spaces and the like. This provides sufficient motivation to researchers to review various concepts and results. The theory of ternary algebraic system was introduced by D. H. Lehmer [11]. He investigated certain ternary algebraic systems called triplexes which turn out to be commutative ternary groups. The notion of ternary semigroups was introduced by Banach S. He showed by an example that a ternary semigroup does not necessarily reduce to an ordinary semigroups. In another hand, in mathematics, Green’s relations characterise the elements of a semigroup in terms of the principal ideals they generate. John Mackintosh Howie, a prominent semigroup theorist, described this work as so all-pervading that, on encountering a new semigroup, almost the first question o...
Classification of Monogenic Ternary Semigroups
2018
The aim of this paper is to classify all monogenic ternary semigroups, up to isomorphism. We divide them to two groups: finite and infinite. We show that every infinite monogenic ternary semigroup is isomorphic to the ternary semigroup O, the odd positive integers with ordinary addition. Then we prove that all finite monogenic ternary semigroups with the same index and the same period are isomorphic. We also investigate structure of finite monogenic ternary semigroups and we prove that any finite monogenic ternary semigroup is isomorphic to a quotient ternary semigroup.
SPECIAL TYPES OF TERNARY SEMIGROUPS
x T\U or T is a simple ternarysemigroup. Definition 2.1: Let T ≠ . Then T is called a ternarysemigroup if being existence a mapping from T T T to T which maps (pqr) [ pqr] satisfying the condition :[(pqr) st] = [ p(qrs)t] = [pq(rst)] for all p, q, r, s, t T. Definition 2.2: An idempotent component e T is said to be left (or lateral or right) identity of the if eaa = a(or aea = a or aae = a) for all a T. Left (or lateral or right) identity may not be unique. But if e is an identity (i.e. e plays the role of left lateral and right identity simultaneously) then e is unique. V. Jyothi et al.
Semihypergroups associated with ternary relations
Afrika Matematika, 2018
Davvaz and Leoreanu-Fotea (Commun Algebra 38(10):3621-3636, 2010) studied binary relations on ternary semihypergroups. A ternary relation or triadic relation is a relation in which the number of places in the relation is three. Now, in this paper, instead of binary relations we consider ternary relations and instead of ternary semihypergroups we consider ordinary semihypergroups. Then, we study ternary relations on semihypergroups. In particular, we discuss some properties of compatible ternary relations on them.