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.

in the transformation semigroup (x, s) we introduce the height of a closed nonempty invariant subset of x, define the transformed dimension of nonempty subset s of x and obtain some results and relations.

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.

In the transformation semigroup (X, S) we introduce the height of a closed nonempty invariant subset of X, define the transformed dimension of nonempty subset S of X and obtain some results and relations.

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...

this text carries out some ideas about exact and p− exact sequences of transformationsemigroups. some theorems like the short five lemma (lemma 1.3 and lemma 2.3) are valid here as inexact sequences of r − modules.

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).