Some results in constructive semigroup theory

Abstract

We give a constructive treatment of some basic concepts and results in semigroup theory. Focusing on semigroups equipped with an apartness relation, we give analogues, from the point of view of apartness, of several classical constructions and results, including transitive closure and congruence closure, free semigroups, periodicity, Rees factors, and Green's relations.

V2: Major re-write of Section 3, due to an error in v1: Proposition 3.11. Other minor updates. 33 pages