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

Authors : Pascual JARA

Pages : 1-20

Doi:10.24330/ieja.1300716

View : 38 | Download : 56

Publication Date : 2023-07-10

Article Type : Research Paper

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