Gamma-semigroups with Unities and Morita Equivalence for Monoids

Sujit Kumar Sardar, Sugata Gupta, Kar Ping Shum

Abstract

In this paper we show that the left operator and right operator semi groups of a Γ-semigroup with unities are Morita equivalent monoids. It is also deduced that if L and R are two Morita equivalent monoids then a Γ-semigroup with unities can be constructed such that its left and right operator monoids are isomorphic to L and R respectively. This result is used to obtain some properties of monoids which remain invariant under Morita equivalence. 

Keywords

$\Gamma$-semigroup, Morita equivalence for monoids, Morita invariant.

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