An extension of $S$-noetherian rings and modules

Pascual Jara

An extension of $S$-noetherian rings and modules

Commutative Algebra 2020-11-06 v1

Authors: Pascual Jara

Abstract

For any commutative ring $A$ we introduce a generalization of $S$ -noetherian rings using a hereditary torsion theory $\sigma$ instead of a multiplicatively closed subset $S\subseteq{A}$ . It is proved that if $A$ is a totally $\sigma$ -noetherian ring, then $\sigma$ is of finite type, and that totally $\sigma$ -noetherian is a local property.

Keywords

commutative ring s-noetherian ring hereditary torsion theory totally sigma-noetherian finite type local property

Cite

@article{arxiv.2011.03008,
  title  = {An extension of $S$-noetherian rings and modules},
  author = {Pascual Jara},
  journal= {arXiv preprint arXiv:2011.03008},
  year   = {2020}
}

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