Completely semiprime hyperideals in ternary semi hypergroups (original) (raw)
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Pseudo Symmetric Ideals In Ternary Semigroups
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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.
Abul Basar, Annals of Communications in Mathematics, 3(1), 63-79, 2020
The aim of the present paper is to define and bring together the fundamental definitions such as relative hyperideals, relative bi-hyperideals, relative quasi-hyperideals, relative prime hyperideals, relative weakly prime hyperideals, relative semiprime hyperideals, relative prime and relative semiprime bi-hyperideals, and hyper relative regularity of dynamic algebraic character to develop the theory of hypersemigroups, and obtain the results relating to and connecting these hyperideal-theoretic definitions of this vast theory to the larger framework of the algebraic area of ordered hypersemigroups as well as of involution ordered hypersemigroups.
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Special Types of Ternary Semigroups
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Abstract: 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 U-ternarysemigroup 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.