Preliminaries on PI-Algebras
Jan Okniński · 2020
This chapter discusses the results known for PI -semigroup algebras. It extends some facts on PI -group algebras and on semigroup algebras of arbitrary commutative semigroups. The chapter repeatedly uses some fundamental results on the semi-simple and radical parts of a PI -algebra. If an algebra R satisfies an identity of degree n , then R satisfies a multilinear identity of degree n . The chapter provides an example to show that one may expect a characterization of the PI -property for semigroup algebra in terms of semigroup and the characteristic of the field only. It also presents a standard connection between the PI -properties in distinct characteristics.