Abstract

Let S be a linear algebraic semigroup defined over a field. The kernel of S, denoted ker(S ), as the minimal two-sided semigroup-theoretical ideal of S, exists and is a Zariski closed subset of M. In many situations, certain properties of a linear algebraic monoid are controlled to a large degree by the structure of its kernel. In this paper, the structure of the kernel of S is described in terms of algebraic group, algebraic variety and the Rees construction. Some properties of an irreducible algebraic monoid related to ker(M ) are studied.