On the local finite separability of finitely generated associative rings

Abstract

It is proved that analogs of the theorems of M. Hall and N. S. Romanovskii are not true in the class of commutative rings. Necessary and sufficient conditions for the local finite separability of monogenic rings are established. As a corollary, it is proved that a finitely generated torsion-free PI-ring is locally finitely separable if and only if its additive group is finitely generated.