A left almost semigroup (LA-semigroup) or an Abel-Grassmann’s groupoid (AG-groupoid) is investigated in several papers. In this paper we have discussed ideals in LA-semigroups. Specifically, we have shown that every ideal in an LA-semigroup S with left identity e is prime if and only if it is idempotent and the set of ideals of S is totally ordered under inclusion. We have shown that an ideal o...

In this paper, the concept of (∈,∈ ∨ qk)-fuzzy quasi-ideals of an ordered semigroup S is introduced by the ordered fuzzy points of S, which is a generalization of fuzzy quasi-ideal of S, and related properties are investigated. Furthermore, we introduce the concepts of prime and completely semiprime (∈,∈ ∨ qk)-fuzzy quasi-ideals of ordered semigroups, and characterize bi-regular ordered semigro...

It is well known that the right (left) regular, regular, and intra-regular ordered semigroups play an essential role in studying the structure, especially the decomposition, of ordered semigroups. In the present paper we study some more general classes containing the right regular, left regular, regular and intra-regular ordered semigroups. As an application of our results we get characterizati...

In this paper an extensive study of the concepts generalized Green’s relations and GV -semigroups without order to ordered semigroups have been given. Our approach allows one see nature in class -ordered semigroups. Moreover we show that semigroup S is a if only complete semilattice completely π-regular Archimedean

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.

Algebraic structures especially an ordered semigroups play a prominent role in mathematics with wide ranging applications in many disciplines such as control engineering, computer arithmetics, coding theory, sequential machines and formal languages. A theory of fuzzy sets in terms of fuzzy points on ordered semigroups can be developed. In this paper, we generalize the concept of (α, β)-fuzzy le...

The purpose of this paper is to characterize an ordered semigroup S in terms the properties associated B(S) all bi-ideals S. We show that a Clifford if and only semilattice. normal band both regular intra regular. For each subvariety V bands, we such ∈ V.

We study C*-algebras associated with subsemigroups of groups. For a large class of such semigroups including positive cones in quasi-lattice ordered groups and left Ore semigroups, we describe the corresponding semigroup C*algebras as C*-algebras of inverse semigroups, groupoid C*-algebras and full corners in associated group crossed products. These descriptions allow us to characterize nuclear...

In this paper, we first introduce the new concept of completely semiprime fuzzy ideals of an ordered semigroup S, which is an extension of completely semiprime ideals of ordered semigroup S, and investigate some its related properties. Especially, we characterize an ordered semigroup that is a semilattice of simple ordered semigroups in terms of completely semiprime fuzzy ideals of ordered semi...

In this paper, the concept of semiprimary fuzzy ideals of an ordered semigroup S is introduced. Some characterizations for an ordered semigroup S to be a semilattice of archimedean (rarchimedean, t-archimedean) ordered subsemigroups are given by some binary relations on S and the fuzzy radical of fuzzy ideals (fuzzy right ideals, fuzzy bi-ideals) of S. Furthermore, some characterizations for an...