ON GREEN'S EQUIVALENCES IN Γ -GROUPOIDS.

This paper deals with Γ-groupoids which are generalizations of groupoids and Γ- semigroups. The main purpose of this paper is to extend Green's equivalences and Green's Lemma to suitably restricted Γ-groupoids. We study only Γ-groupoids satisfying some additional conditions and we show that these are sufficient for the statement of Green's equivalences in case of Γ-groupoids. Additional condition sufficient to prove Green's Lemma for Γ-groupoids is provided and some illustrative examples are presented. [ABSTRACT FROM AUTHOR]