S-Artinian rings and finitely S-cogenerated rings

No Thumbnail Available

Date

2020

Journal Title

Journal ISSN

Volume Title

Publisher

World Scientific Publ Co Pte Ltd

Access Rights

info:eu-repo/semantics/closedAccess

Abstract

Let R be a commutative ring with nonzero identity and S subset of R be a multiplicatively closed subset. In this paper, we study S-Artinian rings and finitely S-cogenerated rings. A commutative ring R is said to be an S-Artinian ring if for each descending chain of ideals {In}(n is an element of N) of R, there exist s is an element of S and k is an element of N such that sI(k) subset of I-n for all n >= k. Also, R is called a finitely S-cogenerated ring if for each family of ideals {I alpha}(alpha)(is an element of Delta) of R, = where Delta is an index set, boolean AND(alpha is an element of Delta) I alpha implies = 0 implies s(boolean AND(alpha is an element of Delta), I alpha) = 0 for some s is an element of S and a finite subset Delta' subset of Delta. Moreover, we characterize some special rings such as Artinian rings and finitely cogenerated rings. Also, we extend many properties of Artinian rings and finitely cogenerated rings to S-Artinian rings and finitely S-cogenerated rings.

Description

Keywords

Artinian Ring, Finitely Cogenerated Ring, S-Artinian Ring, Finitely S-Cogenerated Ring, Noetherian Rings

Journal or Series

Journal of Algebra and Its Applications

WoS Q Value

Q3

Scopus Q Value

Q2

Volume

19

Issue

3

Citation