An extension of s-noetherian rings and modules Jara Martínez, Pascual 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 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 fi nite type. 2024-11-25T07:56:07Z 2024-11-25T07:56:07Z 2023 journal article International Electronic Journal of Algebra. Volume 34 (2023) 1-20 https://hdl.handle.net/10481/97297 10.24330/ieja.1300716 eng http://creativecommons.org/licenses/by-nc-nd/3.0/ open access Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License