On the finite separability of finitely generated commutative rings

2023/10/05 by Kublanovsky, Stanislav
#13F20 13F10 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2310.03868

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.

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