PI-Semigroup Algebras
Jan Okniński · 2020
This chapter discusses the basic classes of semigroups for which necessary and sufficient conditions for the PI -property of the corresponding semigroup algebras may be given. The permutational property alone does not seem to be the right way to attack the problem of characterizing the PI -property of semigroup algebras of finitely generated semisimple semigroups that are not groups. Since semisimple semigroups with PI -semigroup algebras must be completely semisimple, the chapter proposes a way of relating the PI -property of semigroup algebra to the PI -property of some group algebras. It also presents a particular case, in which the PI -property may be checked locally—through the principal factor algebras.