Dominions and Zigzag theorem for $\Gamma$-semigroups

Abstract

Dominions have been studied from different perspectives however their major application lies to study the closure property for monoids. The most useful characterization of semigroup domonions is provided by the famous Isbell’s Zigzag Theorem. In this paper, we introduce the dominion of a  $\Gamma$-semigroups and give the analogue of Isbell's zigzag theorem in  $\Gamma$-semigroups.