In this paper we give a structural characterization for semigroups whose power semigroups are 0-Archimedean. We prove that these semigroups are exactly the nilpotent semigroups.

In this paper we extend some results concerning ideals of left regular and intra-regular ordered semigroups to fuzzy ordered semigroups. A theory of fuzzy sets on ordered groupoids and ordered semigroups can be developed. Some results on ordered groupoidssemigroups have been already given by the same authors. The aim of writing this paper is to show the way we pass from the theory of ordered se...

Let T(X) be the full transformation semigroup on a nonempty set X. For ? Z Y X, let T(X,Y,Z) = {? T(X):Y? Z}. It is not difficult to see that it generalized form of three well-known semigroups. This paper obtains an isomorphism theorem T(X,Y,Z). In addition, when X finite and rank calculated.

This paper applies the concept of FA-presentable structures to semigroups. We give a complete classification of the finitely generated FA-presentable cancellative semigroups: namely, a finitely generated cancellative semigroup is FA-presentable if and only if it is a subsemigroup of a virtually abelian group. We prove that all finitely generated commutative semigroups are FA-presentable. We giv...

In this paper we give a characterization for all semigroups whose square is a group. Moreover, we axiomatize such semigroups and study some relations between the class of these semigroups and Grouplikes,introduced by the author. Also, we observe that this paper characterizes and axiomatizes a class of Homogroups (semigroups containing an ideal subgroup).  Finally, several equivalent conditions ...

Within the usual semidirect product S ∗ T of regular semigroups S and T lies the set Reg (S ∗ T ) of its regular elements. Whenever S or T is completely simple, Reg (S ∗T ) is a (regular) subsemigroup. It is this ‘product’ that is the theme of the paper. It is best studied within the framework of existence (or e-) varieties of regular semigroups. Given two such classes, U and V, the e-variety U...

It is well known that intra-regular semigroups (ordered semigroups) play an essential role in studying the structure of semigroups (ordered semigroups). In this paper we present a structure theorem referring to the decomposition of ordered semigroups into left strongly simple components, that is, into components, which are both simple and left quasi-regular. We prove, among others, that if an o...

Left restriction semigroups have appeared at the convergence of several flows of research, including the theories of abstract semigroups, of partial mappings, of closure operations and even in logic. For instance, they model unary semigroups of partial mappings on a set, where the unary operation takes a map to the identity map on its domain. This perspective leads naturally to dual and two-sid...

In this paper we define C-induced action graph G(S,a,C;A) corresponding to a semigroup act (S,a,A) and subset C of S. This generalizes many interesting graphs including Cayley Graph groups semigroups, Transformation Graphs (TRAG), Group Action (GAG), Derangement Graphs, Directed Power Semigroups etc. We focus on the case when = S name digraph, so obtained, as Semigroup Act (S, a, A). Some basic...