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.

Let S be a regular semigroup and let p be a congruence relation on S. The kernel of p, in notation kerp, is the union of the idempotent p-classes. The trace of p, in notation trp, is the restriction of p to the set of idempotents of S. The pair (kerp,trp) is said to be the congruence pair associated with p. Congruence pairs can be characterized abstractly, and it turns out that a congruence is ...

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 ...

Exactly as in semigroups, Green’s relations play an important role in the theory of ordered semigroups—especially for decompositions of such semigroups. In this paper we deal with the -trivial ordered semigroups which are defined via the Green’s relation , and with the nil and Δ-ordered semigroups. We prove that every nil ordered semigroup is -trivial which means that there is no ordered semigr...

A concept of ideal extensions in ternary semigroups is introduced and throughly investigated. The connection between an ideal extensions and semilattice congruences in ternary semigroups is considered.

Consider an interval I ⊆ Q . Set S(I) = {m ∈ N : ∃ n ∈ N , mn ∈ I}. This turns out to be a numerical semigroup, and has been the subject of considerable recent investigation (see Chapter 4 of [2] for an introduction). Special cases include modular numerical semigroups (see [4]) where I = [mn , m n−1 ] (m,n ∈ N ), proportionally modular numerical semigroups (see [3]) where I = [mn , m n−s ] (m,n...

Among the most important and intensively studied classes of semigroups are finite semigroups, regular semigroups and inverse semigroups. Finite semigroups arise as syntactic semigroups of regular languages and as transition semigroups of finite automata. This connection has lead to a large and deep literature on classifying regular languages by means of algebraic properties of their correspondi...

The concept of an automaton group generalizes easily to semigroups, and the systematic study of this area is beginning. This paper aims to contribute to that study. The basic theory of automaton semigroups is briefly reviewed. Various natural semigroups are shown to arise as automaton semigroups. The interaction of certain semigroup constructions with the class of automaton semigroups is studie...

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.