Finite Nilpotent Semigroups of Small Coclass

Ashs Theorem, Finite Nilpotent Semigroups, and One-Dimensional Tiling Semigroups

This is the manuscript for a talk given at CAUL (19 October, 2001) and also at Northern Illinois University (26 July, 2002). I am grateful to CAUL for their generous support during my visit there in October/November 2001) and to the Department of Mathematical Sciences at NIU (in particular to W.D. Blair) for the mini-conference on the occasion my my retirement.

On nilpotent subsemigroups in some matrix semigroups

We describe maximal nilpotent subsemigroups of a given nilpotency class in the semigroup Ωn of all n × n real matrices with nonnegative coefficients and the semigroup Dn of all doubly stochastic real matrices.

Dynamics of Finite Semigroups

Dualisability of Finite Semigroups

We describe the inherently non-dualisable finite algebras from some semigroup related classes. The classes for which this problem is solved include the variety of bands, the pseudovariety of aperiodic monoids, commutative monoids, and (assuming a reasonable conjecture in the literature) the varieties of all finite monoids and finite inverse semigroups. The first example of an inherently non-dua...

Decidability and Tameness in the Theory of Finite Semigroups