Semigroup Algebras That Are Principal Ideal Rings Original Research Article

It is shown that a semigroup algebraK[S] which is a principal left ideal ring is a finitely generated PI-algebra of Gelfand–Kirillov dimension at most 1. A complete description of principal (left and right) ideal ringsK[S], and of the underlying semigroupsS, is obtained. Semiprime principal left ideal ringsK[S] are shown to be principal right ideal rings and a description of this class of rings follows.