Noetherian Rings and Their Extensions

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 ∈ S and a finitely generated submodule F of M such that Ns ⊆ F ⊆ N, and R is called a right S-Noetherian...

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Bibliographic Details
Published in:Taiwanese journal of mathematics 2016-12, Vol.20 (6), p.1231-1250
Main Authors: Baeck, Jongwook, Lee, Gangyong, Lim, Jung Wook
Format: Article
Language:English
Subjects:
Mathematical rings
Power series
Online Access:Get full text
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Summary: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 ∈ S and a finitely generated submodule F of M such that Ns ⊆ F ⊆ N, and R is called a right S-Noetherian ring if RRis 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.
ISSN:1027-5487
2224-6851