We define the notion of weakly ordered semigroups. For this class of semigroups, we compute the radical of the semigroup algebras. This generalizes some results on left regular bands and on 0Hecke algebras.

We prove that the decision problem of whether or not a finite semigroup has the representation extension property is decidable. 1. The main theorem and preliminaries It is an immediate consequence of the normal form theorem for amalgamated free products of groups that every amalgam of groups embeds in some group. However, this result fails for semigroup amalgams: an early result of Kimura [6] s...

LetP be a semigroup that admits an embedding into a groupG.Assume that the embedding satisfies the Toeplitz condition recently introduced by the third named author and that the Baum–Connes conjecture holds for G. We prove a formula describing the K-theory of the reduced crossed product A α,r P by any automorphic action of P . This formula is obtained as a consequence of a result on the K-theory...

Regular semigroups and their structures are the most wonderful part of semigroup theory, contents very rich. In order to explore more regular semigroups, this paper extends relevant classical conclusions from a new perspective: by transforming positions elements in regularity conditions, some conditions (collectively referred as transposition regularity) obtained, concepts various introduced (L...

In this paper we introduce bipolar fuzzy subsemigroup, bipolar fuzzy left (right) ideals and bipolar fuzzy bi-ideal in ordered semigroups. We characterize different classes of ordered semigroups by the properties of their bipolar fuzzy ideals and bipolar fuzzy bi-ideals.

In this paper, we discuss the hypothesis that an ordered Γ-semigroup can be constructed on M-left(right)-tri-basis. order to generalize left(right)-tri-basis using Γ-semigroups and semigroups, examined M-tri-ideals from a purely algebraic standpoint. We also present form of M-tri-ideal generator. investigated M-left(right)-tri-ideal Γ-semigroup. obtain their properties, used It was possible gen...

For a nonempty set X, let T(X) be the total transformation semigroup on X. In this paper, we consider subsemigroups of which are defined by T(X,Y) ={α∈T(X):Xα⊆Y}andS(X,Y)={α∈T(X):Yα⊆Y} where Y is non-empty subset We characterize left regular and right elements both S(X,Y). Moreover, necessary sufficient conditions for S(X,Y) to given. These results then applied determine numbers in finite

In this paper, a new approach to LA-semigroup theory is proposed by obtaining significant characterizations of regular, intra-regular, completely regular, weakly regular and quasi-regular LA-semigroups via soft intersection left (right, two-sided) ideals, (generalized) bi-ideals, interior ideals, quasi-ideals of LA-semigroups.