A note on weakly s-noetherian rings

Dong Kyu Kim; Jung Wook Lim

doi:10.3390/sym12030419

A note on weakly s-noetherian rings

Dong Kyu Kim, Jung Wook Lim

Kyungpook National University

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

Let R be a commutative ring with identity and S a (not necessarily saturated) multiplicative subset of R. We call the ring R to be a weakly S-Noetherian ring if every S-finite proper ideal of R is an S-Noetherian R-module. In this article, we study some properties of weakly S-Noetherian rings. In particular, we give some conditions for the Nagata's idealization and the amalgamated algebra to be weakly S-Noetherian rings.

Original language	English
Article number	419
Journal	Symmetry
Volume	12
Issue number	3
DOIs	https://doi.org/10.3390/sym12030419
State	Published - 1 Mar 2020

Keywords

Amalgamated algebra along an ideal
Nagata's idealization
S-finite
S-Noetherian module
Weakly S-Noetherian ring

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10.3390/sym12030419

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AB - Let R be a commutative ring with identity and S a (not necessarily saturated) multiplicative subset of R. We call the ring R to be a weakly S-Noetherian ring if every S-finite proper ideal of R is an S-Noetherian R-module. In this article, we study some properties of weakly S-Noetherian rings. In particular, we give some conditions for the Nagata's idealization and the amalgamated algebra to be weakly S-Noetherian rings.

KW - Amalgamated algebra along an ideal

KW - Nagata's idealization

KW - S-finite

KW - S-Noetherian module

KW - Weakly S-Noetherian ring

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JF - Symmetry

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ER -

A note on weakly s-noetherian rings

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Keywords

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