S-Noetherian Properties of Composite Ring Extensions

Jung Wook Lim; Dong Yeol Oh

doi:10.1080/00927872.2014.904329

S-Noetherian Properties of Composite Ring Extensions

Jung Wook Lim
, Dong Yeol Oh

Chosun University

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

30 Scopus citations

Abstract

Let R be a commutative ring with identity and S a multiplicative subset of R. We say that R is an S-Noetherian ring if for each ideal I of R, there exist an s ∈ S and a finitely generated ideal J of R such that sI ⊆ J ⊆ I. In this article, we study transfers of S-Noetherian property to the composite semigroup ring and the composite generalized power series ring.

Original language	English
Pages (from-to)	2820-2829
Number of pages	10
Journal	Communications in Algebra
Volume	43
Issue number	7
DOIs	https://doi.org/10.1080/00927872.2014.904329
State	Published - 3 Jul 2015

Keywords

D + E[Γ*]
D + [[E ]]
S-Noetherian ring, S-Noetherian module

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10.1080/00927872.2014.904329

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title = "S-Noetherian Properties of Composite Ring Extensions",

abstract = "Let R be a commutative ring with identity and S a multiplicative subset of R. We say that R is an S-Noetherian ring if for each ideal I of R, there exist an s ∈ S and a finitely generated ideal J of R such that sI ⊆ J ⊆ I. In this article, we study transfers of S-Noetherian property to the composite semigroup ring and the composite generalized power series ring.",

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N2 - Let R be a commutative ring with identity and S a multiplicative subset of R. We say that R is an S-Noetherian ring if for each ideal I of R, there exist an s ∈ S and a finitely generated ideal J of R such that sI ⊆ J ⊆ I. In this article, we study transfers of S-Noetherian property to the composite semigroup ring and the composite generalized power series ring.

AB - Let R be a commutative ring with identity and S a multiplicative subset of R. We say that R is an S-Noetherian ring if for each ideal I of R, there exist an s ∈ S and a finitely generated ideal J of R such that sI ⊆ J ⊆ I. In this article, we study transfers of S-Noetherian property to the composite semigroup ring and the composite generalized power series ring.

KW - D + E[Γ]

KW - D + [[E ]]

KW - S-Noetherian ring, S-Noetherian module

UR - https://www.scopus.com/pages/publications/84930607437

U2 - 10.1080/00927872.2014.904329

DO - 10.1080/00927872.2014.904329

M3 - Article

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VL - 43

SP - 2820

EP - 2829

JO - Communications in Algebra

JF - Communications in Algebra

IS - 7

ER -

S-Noetherian Properties of Composite Ring Extensions

Abstract

Keywords

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