A new semigroup obtained via known ones

Abstract

The goal of this paper is to establish a new class of semigroups based on both Rees matrix and completely [Formula: see text]-simple semigroups. We further present some fundamental properties and finiteness conditions for this new semigroup structure.

On Classification of Semigroup N by Green’s Theorem

“…en, we obtained N which satisfies important homological properties and proved that the spined product of the (C)-inversive semigroup and the idempotent semigroup of N is isomorphic to the strictly inverse semigroup N in [1]. Furthermore, we gave some consequences of the results to make a detailed classification over N in the same reference.…”

“…It is well known that certain equivalence relations L and R for an arbitrary semigroup S were first introduced by Green [10], in which those are defined in a very influential method to make a classification for a new semigroup. As a result of this fact, in [1], we studied L and R-Green's relations for N. On the other hand, we will prove Green's lemma and Green's theorem by developing the results which are obtained in [1].…”

“…It is good to keep in mind the de nition of the semigroup N given in [1], in order to grasp the importance of this paper. Since this paper is continuation of our work in [1], let us recall the basic facts regarding the semigroup N.…”

Some Indices over a New Algebraic Graph

“…For example, in [3], the author considered a new product and gave some properties on a special product of semigroups (and monoids). Similarly, in [4], we established a new class of semigroups N based on both Rees matrix and completely 0-simple semigroups. We further presented some fundamental properties and finiteness conditions for this new structure.…”

“…Here, every r i and c k are elements of Rees matrix semigroup (M R ) and completely 0-simple semigroup (M C ), respectively. Actually, we know that the semigroup N consists of the semigroup S and the group G (see [4] for more details). Moreover, we can keep in our mind the diagram in Figure 1 for the semigroup N.…”