An extension of $S$--noetherian rings and modules

Year 2023, Volume: 34 Issue: 34, 1 - 20, 10.07.2023

Pascual Jara

https://doi.org/10.24330/ieja.1300716

Abstract

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

Keywords

Noetherian ring and module, polynomial ring, formal power series ring

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