Variants of finite full transformation semigroups

On certain semigroups of transformations that preserve double direction equivalence

Let TX be the full transformation semigroups on the set X. For an equivalence E on X, let TE(X) = {α ∈ TX : ∀(x, y) ∈ E ⇔ (xα, yα) ∈ E}It is known that TE(X) is a subsemigroup of TX. In this paper, we discussthe Green's *-relations, certain *-ideal and certain Rees quotient semigroup for TE(X).

UNIVERSAL COMPACTIFICATIONS OF TRANSFORMATION SEMIGROUPS

We extend the notion of semigroup compactification to the class of transformation semigroups, and determine the compactifications which are universal with respect to some topological properties.

Automorphisms of partial endomorphism semigroups

In this paper we propose a general recipe for calculating the automorphism groups of semigroups consisting of partial endomorphisms of relational structures with a single m-ary relation for any m ∈ N over a finite set. We use this recipe to determine the automorphism groups of the following semigroups: the full transformation semigroup, the partial transformation semigroup, and the symmetric in...

Semigroups of rectangular matrices under a sandwich operation

Let Mmn =Mmn(F) denote the set of all m× n matrices over a field F, and fix some n×m matrix A ∈ Mnm. An associative operation ? may be defined on Mmn by X ? Y = XAY for all X,Y ∈ Mmn, and the resulting sandwich semigroup is denoted Mmn = Mmn(F). In this article, we study Mmn as well as its subsemigroups Reg(Mmn) and EA mn (consisting of all regular elements and products of idempotents, respecti...

Decidability and Tameness in the Theory of Finite Semigroups