E-Inversive Γ-Semigroups

• Journal title : Kyungpook mathematical journal
• Volume 49, Issue 3,  2009, pp.457-471
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2009.49.3.457
Title & Authors
E-Inversive Γ-Semigroups

Abstract
Let S = {a, b, c, ...} and $\small{{\Gamma}}$ = {$\small{{\alpha}}$, $\small{{\beta}}$, $\small{{\gamma}}$, ...} be two nonempty sets. S is called a $\small{{\Gamma}}$-semigroup if $\small{a{\alpha}b{\in}S}$, for all $\small{{\alpha}{\in}{\Gamma}}$ and a, b $\small{{\in}}$ S and $\small{(a{\alpha}b){\beta}c=a{\alpha}(b{\beta}c)}$, for all a, b, c $\small{{\in}}$ S and for all $\small{{\alpha}}$, $\small{{\beta}}$ $\small{{\in}}$ $\small{{\Gamma}}$. An element $\small{e{\in}S}$ is said to be an $\small{{\alpha}}$-idempotent for some $\small{{\alpha}{\in}{\Gamma}}$ if $\small{e{\alpha}e}$ = e. A $\small{{\Gamma}}$-semigroup S is called an E-inversive $\small{{\Gamma}}$-semigroup if for each $\small{a{\in}S}$ there exist $\small{x{\in}S}$ and $\small{{\alpha}{\in}{\Gamma}}$ such that a$\small{{\alpha}}$x is a $\small{{\beta}}$-idempotent for some $\small{{\beta}{\in}{\Gamma}}$. A $\small{{\Gamma}}$-semigroup is called a right E-$\small{{\Gamma}}$-semigroup if for each $\small{{\alpha}}$-idempotent e and $\small{{\beta}}$-idempotent f, $\small{e{\alpha}}$ is a $\small{{\beta}}$-idempotent. In this paper we investigate different properties of E-inversive $\small{{\Gamma}}$-semigroup and right E-$\small{{\Gamma}}$-semigroup.
Keywords
E-inversive $\small{{\Gamma}}$-semigroup;Right E-$\small{{\Gamma}}$-semigroup;semidirect product;
Language
English
Cited by
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