ABSTRACT
This chapter presents the study of the Jacobson radical of semigroup algebras satisfying polynomial identities. The Jacobson radical of a finitely generated PI-algebra is a nilpotent ideal. Thus, the hypothesis on the existence of a multiplicative basis in an algebraic leads to a consequence related to that obtained in the finitely generated case. A special case of interest arises when considering separative semigroups. The chapter offers an interesting technique coming from a general result on semilattices of semigroups. It also extends the description of Jacobson radical for commutative semigroup in terms of some cancellative semigroups arising from the commutative semigroup.
