On Relative Ranks of Finite Transformation Semigroups with Restricted Range

The Ranks of Some Transformation Semigroups on a Finite Set

compactifications and representations of transformation semigroups

this thesis deals essentially (but not from all aspects) with the extension of the notion of semigroup compactification and the construction of a general theory of semitopological nonaffine (affine) transformation semigroup compactifications. it determines those compactification which are universal with respect to some algebric or topological properties. as an application of the theory, it is i...

Diagonal Ranks of Semigroups

We introduce the notion of diagonal ranks of semigroups, which are numerical characteristics of semigroups. Some base properties of diagonal ranks are obtained. A new criterion for a monoid being a group is obtained using diagonal ranks. For some semigroup classes we investigate whether their diagonal acts are finitely generated or not. For the semigroups of full transformations, partial transf...

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.

Variants of finite full transformation semigroups

The variant of a semigroup S with respect to an element a ∈ S, denoted S, is the semigroup with underlying set S and operation ? defined by x ? y = xay for x, y ∈ S. In this article, we study variants T a X of the full transformation semigroup TX on a finite set X. We explore the structure of T a X as well as its subsemigroups Reg(T a X) (consisting of all regular elements) and E X (consisting ...