Orthodox Γ‐semigroups

Abstract

LetM={a,b,c,…}andΓ={α,β,γ,…}be two non-empty sets.Mis called aΓ-semigroup ifaαb∈M, forα∈Γandb∈Mand(aαb)βc=aα(bβc), for alla,b,c∈Mand for allα,β∈Γ. A semigroup can be considered as aΓ-semigroup. In this paper we introduce orthodoxΓ-semigroups and extend different results of orthodox semigroups to orthodoxΓ-semigroups.

On inf -Hesitant Fuzzy Γ -Ideals of Γ -Semigroups

“…In 1981, Sen [17] introduced the concept and notion of the Γ-semigroup as a generalization of the plain semigroup and ternary semigroup. Many classical notions and results of (ternary) semigroups have been extended and generalized to Γ-semigroups, by many mathematicians, for instance, Siripitukdet and Iampan [18,19], Siripitukdet and Julatha [20], Dutta and Adhikari [21,22], Saha and Sen [23][24][25], Hila [26,27], and Chinram [28,29]. Simuen, Iampan, Chinram, Sardar, Majumder, Dutta, and Davvaz [30][31][32][33][34][35] studied theory of Γ-semigroups via fuzzy subsets.…”

Lattice ordered semigroups andΓ-hypersemigroups

“…One can find this definition of Γ -semigroups in [21] where the notion of a radical in a Γ -semigroup and the notion of ΓS -act over a Γ -semigroup have been introduced, in [19] and [20] where the notions of regular and orthodox Γ -semigroups have been introduced and studied and in [16] where the maximum idempotentseparating congruence on an inverse Γ -semigroup has been studied. But still, we cannot say that Γ is a set of binary operations on M to work on it.…”

A Hesitant Fuzzy Set Approach to Ideal Theory in Γ-Semigroups

“…In 1981, Sen [17] introduced the concept and notion of the Γ-semigroup as a generalization of plain semigroup and ternary semigroup. Many classical notions and results of the theory of semigroups have been extended and generalized to Γ-semigroups, by many mathematicians, for instance, Dutta and Adhikari [18,19], Saha and Sen [20][21][22], and Hila [23][24][25]. Mustafa et al [26] have introduced the Γsemigroup in terms of intuitionistic fuzzy sets.…”