Computational Complexity of Checking Identities in 0-simple Semigroups and Matrix Semigroups over Finite Fields

On the Krohn-rhodes Complexity of Semigroups of Upper Triangular Matrices

We consider the Krohn-Rhodes complexity of certain semigroups of upper triangular matrices over finite fields. We show that for any n > 1 and finite field k, the semigroups of all n × n upper triangular matrices over k and of all n × n unitriangular matrices over k have complexity n− 1. A consequence is that the complexity c > 1 of a finite semigroup places a lower bound of c+1 on the dimension...

The Equational Theory of Ω-terms for Finite R-trivial Semigroups∗

A new topological representation for free profinite R-trivial semigroups in terms of spaces of vertex-labeled complete binary trees is obtained. Such a tree may be naturally folded into a finite automaton if and only if the element it represents is an ω-term. The variety of ω-semigroups generated by all finite R-trivial semigroups, with the usual interpretation of the ω-power, is then studied. ...

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

Brandt extensions and primitive topologically periodic inverse topological semigroups

In this paper we find sufficient conditions on primitive inverse topological semigroup S under which: the inversion inv : (H(S)) (H(S)) is continuous; we show that every topologically periodic countable compact primitive inverse topological semigroups with closed H-classes is topologically isomorphic to an orthogonal sum P i2= Bi (Gi) of topological Brandt extensions Bi (Gi) of countably compac...