Taiwanese Journal of Mathematics

$S$-Noetherian Rings and Their Extensions

Jongwook Baeck, Gangyong Lee, and Jung Wook Lim

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Let $R$ be an associative ring with identity, $S$ a multiplicative subset of $R$, and $M$ a right $R$-module. Then $M$ is called an $S$-Noetherian module if for each submodule $N$ of $M$, there exist an element $s \in S$ and a finitely generated submodule $F$ of $M$ such that $Ns \subseteq F \subseteq N$, and $R$ is called a right $S$-Noetherian ring if $R_R$ is an $S$-Noetherian module. In this paper, we study some properties of right $S$-Noetherian rings and $S$-Noetherian modules. Among other things, we study Ore extensions, skew-Laurent polynomial ring extensions, and power series ring extensions of $S$-Noetherian rings.

Article information

Taiwanese J. Math., Volume 20, Number 6 (2016), 1231-1250.

First available in Project Euclid: 1 July 2017

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Zentralblatt MATH identifier

Primary: 16D25: Ideals 16P99: None of the above, but in this section 16S36: Ordinary and skew polynomial rings and semigroup rings [See also 20M25] 16U20: Ore rings, multiplicative sets, Ore localization

right $S$-Noetherian ring $S$-Noetherian module Hilbert basis theorem Ore extension


Baeck, Jongwook; Lee, Gangyong; Lim, Jung Wook. $S$-Noetherian Rings and Their Extensions. Taiwanese J. Math. 20 (2016), no. 6, 1231--1250. doi:10.11650/tjm.20.2016.7436. https://projecteuclid.org/euclid.twjm/1498874529

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