In this paper we are concerned with the following question: for a semigroup S, what is the largest size of a subsemigroup T ≤ S where T has a given property? The semigroups S that we consider are the full transformation semigroups; all mappings from a finite set to itself under composition of mappings. The subsemigroups T that we consider are of one of the following types: left zero, right zero...

A class of finite semigroups V is said to be decidable if the membership problem for V has a solution, that is, if we can construct an algorithm to test whether a given semigroup lies in V. Decidability of pseudovarieties is not preserved by some of the most common pseudovariety operators, such as semidirect product, Mal’cev product and join [1, 17]. In particular Rhodes [17] has exhibited a de...

The aim of this manuscript is to introduce the \((\alpha,\beta)\)-hesitant fuzzy set and apply it semigroups. In paper, as a generalization concept hesitant sets semigroup theory, subsemigroups semigroups introduced, related properties are discussed. Furthermore, we define study ideals on particular, investigate structure ideal generated by in semigroup. addition, also concepts semiprime semigr...

In this paper, soft intersection LA-semigroups, soft intersection left (right, two-sided) ideals, (generalized) bi-ideals, interior ideals, quasi-ideals in LA-semigroups are defined, their examples and properties are given and their interrelations are obtained.

In this paper, a commutative semigroup will be written as a disjoint union of its cancellative subsemigroups. Based on this fact we will define the left regular representation of a commutative separative semigroup and show that this representation is faithful. Finally concrete examples of commutative separative semigroups, their decompositions and their left regular representations are given.

Right groups are direct products of right zero semigroups and groups and they play a significant role in the semilattice decomposition theory of semigroups. Right groups can be characterized as associative right quasigroups (magmas in which left translations are bijective). If we do not assume associativity we get right quasigroups which are not necessarily representable as direct products of r...

In this paper the concept of Q-fuzzification of ideals of Γ-semigroups has been introduced and some important properties have been investigated. A characterization of regular Γ-semigroup in terms of Q-fuzzy ideals has been obtained. Operator semigroups of a Γ-semigroup has been made to work by obtaining various relationships between Q-fuzzy ideals of a Γ-semigroup and that of its operator semig...

In this paper; we study equations on semidirect products of commutative semigroups. Let Comq,r denote the pseudovariety of all finite semigroups that satisfy the equations xy = yx and x r + q = xr. The pseudovariety Com1,1 is the pseudovariety of all finite semilattices. We consider the product pseudovariety Comq,r * generated by all semidirect products of the form S*T with S ∈ Comq,r and T ∈ ,...