E-Inversive Γ-Semigroups

Mridul Kanti Sen, Sumanta Chattopadhyay
2009 Kyungpook Mathematical Journal  
Let S = {a, b, c, . . . } and Γ = {α, β, γ, . . . } be two nonempty sets. S is called a Γ-semigroup if aαb ∈ S, for all α ∈ Γ and a, b ∈ S and (aαb)βc = aα(bβc), for all a, b, c ∈ S and for all α, β ∈ Γ. An element e ∈ S is said to be an α-idempotent for some α ∈ Γ if eαe = e. A Γ-semigroup S is called an E-inversive Γ-semigroup if for each a ∈ S there exist x ∈ S and α ∈ Γ such that aαx is a β-idempotent for some β ∈ Γ. A Γ-semigroup is called a right E-Γ-semigroup if for each α-idempotent e
more » ... d β-idempotent f , eαf is a β-idempotent. In this paper we investigate different properties of E-inversive Γ-semigroup and right E-Γ-semigroup.
doi:10.5666/kmj.2009.49.3.457 fatcat:3fgjiexzxzaczh5iqhuzblacry