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...

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...

Convolution semigroups of states on a quantum group form the natural noncommutative analogue of convolution semigroups of probability measures on a locally compact group. Here we initiate a theory of weakly continuous convolution semigroups of functionals on a C∗-bialgebra, the noncommutative counterpart of a locally compact semigroup. On locally compact quantum groups we obtain a bijective cor...

In this paper, we introduce generalized adjoint semigroups (GA-semigroups) of a ring R. We construct generalized adjoint semigroups on a ring R by means of bitranslations of R. It is shown that GA-semigroups of a π-regular ring are π-regular. As an application we deduce that in any ring, idempotents can be lifted modulo π-regular ideals. GA-semigroups containing idempotents are described in ter...

In this paper a certain class of polyhedral semigroups which has a presentation $$ is examined‎. ‎The completeness of the presentation and solvability of word problem of this class of semigroups is determined‎. ‎Moreover the combinatorial distance between two words is determined‎.