English

On the finite separability of finitely generated commutative rings

Rings and Algebras 2023-10-09 v1

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 IkI_k where kk is square-free, and IkI_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.

Keywords

Cite

@article{arxiv.2310.03868,
  title  = {On the finite separability of finitely generated commutative rings},
  author = {Stanislav Kublanovsky},
  journal= {arXiv preprint arXiv:2310.03868},
  year   = {2023}
}

Comments

18 pages, in Russian language