On the multiplicative semigroup of a ring
The authors prove that if \(R\) is a PI-ring and if the multiplicative semigroup of \(R\) is finitely generated then \(R\) must be finite. Note that it is well known that if \(R\) is commutative and infinite its multiplicative semigroup is not finitely generated. Whether this is the case or not, for general associative rings, is still an open question.
finitely generated multiplicative semigroups
scientific article; zbMATH DE number 1445782
scientific article