E-Inversive Γ-Semigroups
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Let S = {a, b, c, ...} g and Γ = {α, β, γ, ... } be two nonempty sets. S is called a Γ-semigroup if aαb 2 S, for all α ∈ Γ and a; b 2 S and (aαb)βc = aα(bβc), for all a, b, c 2 ∈ 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 2 S there exist x ∈ S and α 2 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 and β-idempotent f, eαf is a β-idempotent. In this paper we investigate di erent properties of E-inversive Γ-semigroup and right E-Γ-semigroup
Abstract
Let S = {a, b, c, ...} g and Γ = {α, β, γ, ... } be two nonempty sets. S is called a Γ-semigroup if aαb 2 S, for all α ∈ Γ and a; b 2 S and (aαb)βc = aα(bβc), for all a, b, c 2 ∈ 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 2 S there exist x ∈ S and α 2 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 and β-idempotent f, eαf is a β-idempotent. In this paper we investigate di erent properties of E-inversive Γ-semigroup and right E-Γ-semigroup
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