In this paper we introduce R-right (left), L-left (right) cancellative and weakly R(L)-cancellative semigroups and will give some equivalent conditions for completely simple semigroups, (completely) regular right (left) cancellative semigroups, right (left) groups, rectangular groups, rectangular bands, groups and right (left) zero semigroups according to R-right (left), L-left (right) and weak...

decomposability of an algebraic structure into the :union: of its sub-structures goes back to g. scorza's theorem of 1926 for groups. an analogue of this theorem for rings has been recently studied by a. lucchini in 2012. on the study of this problem for non-group semigroups, the first attempt is due to clifford's work of 1961 for the regular semigroups. since then, n.p. mukherjee in ...

We construct  a noncommutative analog of additive functional equations on discrete quantum semigroups and show that this noncommutative functional equation has Hyers-Ulam stability on amenable discrete quantum semigroups. The discrete quantum semigroups that we consider in this paper are in the sense of van Daele, and the amenability is in the sense of Bèdos-Murphy-Tuset. Our main result genera...

in the present paper for a large family of topological semigroups, namely foundation semigroups, for which topological groups and discrete semigroups are elementary examples, it is shown that ?(s) is the dual of a function algebra.

Fuzzy bi-ideals play an important role in the study of ordered semigroupstructures. The purpose of this paper is to initiate and study theintiuitionistic fuzzy bi-ideals in ordered semigroups and investigate thebasic theorem of intuitionistic fuzzy bi-ideals. To provide thecharacterizations of regular ordered semigroups in terms of intuitionisticfuzzy bi-ideals and to discuss the relationships ...

The aim of this paper is to classify all monogenic ternary semigroups, up to isomorphism. We divide them to two groups: finite and infinite. We show that every infinite monogenic ternary semigroup is isomorphic to the ternary semigroup O, the odd positive integers with ordinary addition. Then we prove that all finite monogenic ternary semigroups with the same index...

In 2005, A. Abdollahi and A. Rejali, studied the relations betweenparadoxical decomposition and configuration for semigroups. In thepresent paper, we introduce one other concept of amenability typeon semigroups and groups which includes amenability of semigroupsand inner-amenability of groups. We have extend the previous knownresults to semigroups and groups satisfying this concept.

In  this paper we define the $p$-analog of the restericted reperesentations and also the $p$-analog of the Fourier--Stieltjes algebras on the inverse semigroups . We improve some results about Herz algebras on Clifford semigroups. At the end of this paper we give the necessary and sufficient condition for amenability of these algebras on Clifford semigroups.

generalizing the concepts of -fuzzy (left, right, lateral) ideals, -fuzzy quasi-ideals and   -fuzzy bi (generalized bi-) ideals in ternary semigroups, the notions of -fuzzy (left, right, lateral) ideals, -fuzzy quasi-ideals and -fuzzy bi (generalized bi-) in ternary semigroups are introduced and several related properties are investigated. some new results are obtained.

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 ...