For W a finite set of words, we consider the Rees quotient of a free monoid with respect to the ideal consisting of all words that are not subwords of W . This monoid is denoted by S(W ). It is shown that for every finite set of words W , there are sets of words U ⊃ W and V ⊃ W such that the identities satisfied by S(V ) are finitely based and those of S(U) are not finitely based (regardless of...

The notion of quasi-exact sequence of modules was introduced by B. Davvaz and coauthors in 1999 as a generalization of the notion of exact sequence. In this paper we investigate further this notion. In particular, some interesting results concerning this concept and torsion functor are given.

Geometric semigroup theory is the systematic investigation of finitely-generated semigroups using the topology and geometry of their associated automata. In this article we show how a number of easily-defined expansions on finite semigroups and automata lead to simplifications of the graphs on which the corresponding finite semigroups act. We show in particular that every finite semigroup can b...

Properties such as automaticity, growth and decidability are investigated for the class of finitely generated semigroups which have regular sets of unique normal forms. Knowledge obtained is then applied to the task of demonstrating that a class of semigroups derived from free inverse semigroups under certain closure operations is not automatic. 2000 Mathematics subject classification: primary ...