On local finite separability of finitely generated associative rings

It is proved that analogs of the theorems of M. Hall and N. S. Romanovsky fail in the class of commutative rings. Necessary and sufficient conditions for local finite separability of monogenic rings is 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.