On Classification of Semigroup N by Green’s Theorem

Abstract

In previous papers, it has been recently defined a new class of semigroups based on both Rees matrix and completely 0-simple semigroups. For this new structure, it has been introduced with certain basic properties and finiteness conditions. The main goal of the paper is to prove Green’s Theorem for by indicating the existence of Green’s lemma. We also study generalized Green’s relation over and present some new findings. In particular, we classify our semigroup associated with generalized Green’s relation by constructing good homomorphism.