Identity problems, solvability of equations and unification in varieties of semigroups related to varieties of groups

Abstract

In this survey we consider three kinds of algorithmic questions concerning varieties of semigroups. We are interested in identity problems, in the solvability of a system of equations and in the structure of all solutions of a given system. We study them in significant varieties of semigroups, monoids, groups, completely simple semigroups, completely regular semigroups (in particular semigroups satisfying the identity x r ∈≈∈x) and involutary semigroups (in particular star regular semigroups and inverse semigroups). © 2011 Springer-Verlag Berlin Heidelberg.