Reductive monoids are Von Neumann regular

Abstract

Let k be an algebraically closed field. An a@e algebraic monoid E is an affme algebraic variety, defined over k, together with an associative morphism m: E X E + E and a two-sided unit 1 E E for m. In categorical terminology, an afftne algebraic monoid is a representable functor from the category of afftne varieties to the category of monoids. Algebraic group theory is concerned mainly with reductive groups and their representations whereas the theory of monoids is concerned largely with von Neumann regular monoids. The main result of this paper provides a fundamental link between these two objects.