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arXiv · 2310.03868

On the finite separability of finitely generated commutative rings

Stanislav Kublanovsky
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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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Stanislav Kublanovsky. 2023-10-05. On the finite separability of finitely generated commutative rings. https://arxiv.org/abs/2310.03868

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