Strongly Semicommutative Rings Relative to a Monoid

Abstract

For a monoid M, we introduce strongly M-semicommutative rings obtained as a generalization of strongly semicommutative rings and investigate their properties. We show that if G is a finitely generated Abelian group, then G is torsion free if and only if there exists a ring R with |R| ≥ 2 such that R is strongly G-semicommutative.