Algebraic Semigroups are Strongly π-regular

Abstract

Let $S$ be an algebraic semigroup (not necessarily linear) defined over a field $F$. We show that there exists a positive integer $n$ such that $x^n$ belongs to a subgroup of $S(F)$ for any $x\in S(F)$. In particular, the semigroup $S(F)$ is strongly π-regular.

minor changes, final version