Semigroup algebras of finite inverse semigroups over arbitrary fields

Abstract

In the contracted semigroup algebra A of a finite inverse semigroup S over an arbitrary field there is given a basis, whose elements together with the zero of the algebra A form a semigroup ¯S, which is the 0-direct union of Brandt semigroups, whose description is given in terms of the semigroup S. With the help of this basis there is found the number of nonzero irreducible modular representations of the semigroup S by matrices over an algebraically closed field of nonzero characteristic.