Domain Range Semigroups and Finite Representations

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...

Irreducible Matrix Representations of Finite Semigroups

Munn [9] has shown that for a semigroup S satisfying the minimal condition on principal ideals, there is a natural one-to-one correspondence between irreducible representations of S and irreducible representations vanishing at zero of its 0-simple (or simple) principal factors; for the case of S finite, see Ponizovskii [11]. On the other hand, Clifford, [3] and [4], has obtained all representat...

Decidability and Tameness in the Theory of Finite Semigroups

Domain and Antidomain Semigroups

We axiomatise and study operations for relational domain and antidomain on semigroups and monoids. We relate this approach with previous axiomatisations for semirings, partial transformation semigroups and dynamic predicate logic.

Finite semigroups as categories, ordered semigroups or compact semigroups

The results presented in this section are a good illustration of the following quotation of Marshall Stone [34]: ’A cardinal principle of modern mathematical research may be stated as a maxim: “One must always topologize” ’. Varieties of finite semigroups are a good example where Stone’s principle was applied successfully. Recall that a variety of semigroups is a class of semigroups closed unde...