# Algebra Seminar talk

2011-09-16

Libor **Polak***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).