On the finite separability of finitely generated commutative rings

Abstract

We find necessary and sufficient conditions for the finite separability of finitely generated commutative rings. Namely, we prove that every such ring is a finite extension of its torsion ideal $I_k$ where $k$ is square-free, and $I_k$ is a subdirect product of a finite ring and finitely many zero divisor-free rings of prime characteristic each of which is an entire extension of any of its infinite monogenic subrings.