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 N by indicating the existence of Green’s lemma. We also study generalized Green’s relation over N and present some new findings. In particular, we classify our semigroup N associated with generalized Green’s relation by constructing good homomorphism.

Idealization of a Semigroup by Using Bruck-Reilly Monoids

“…We can briefly remind you of it (We may refer to [26,27] for the details of semi-trivial extensions). As a result, one may study the semitrivial extensions of semigroups via the operation defined in (3). One can also transform the studies in Lemma 3.2 and Theorem 3.3 to arbitrary semigroups without assuming ( ) i SB B  as a monoid.…”

“…Additionally, when we view extensions as a means of combining known structures to create a new structure, this approach yields similar benefits in a distinct and effective manner. As an illustrative example, in [1][2][3], the authors introduced a new semigroup called  and characterized it by extensively studying its properties.…”

New results over Zappa-Szep products via a recent semigroup

“…The other key point of this paper is the semigroup N which was built as an extension of Reesmatrix semigroups by completely zero-simple semigroups. (The detailed studies and propertieson this semigroup see [16,19]). Below, we will briefly recall only the definition of N.…”