Relative ranks of some partial transformation semigroups

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.

Some Notions of Size in Partial Semigroups

In a semigroup, the combinatorial definitions of syndetic, piecewise syndetic, and IP are equivalent to their algebraic characterizations in terms of βS. We introduce the analogous definitions and characterizations of syndetic, piecewise syndetic, and IP for an adequate partial semigroup and show that equivalence between the combinatorial definition and algebraic characterization is lost once w...