When are graded rings graded S-Noetherian rings

Dong Kyu Kim; Jung Wook Lim

doi:10.3390/math8091532

When are graded rings graded S-Noetherian rings

Dong Kyu Kim, Jung Wook Lim

Kyungpook National University

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

6 Scopus citations

Abstract

Let G be a commutative monoid, R = ⊕_α∈Γ R_α a Γ-graded ring and S a multiplicative subset of R₀. We define R to be a graded S-Noetherian ring if every homogeneous ideal of R is S-finite. In this paper, we characterize when the ring R is a graded S-Noetherian ring. As a special case, we also determine when the semigroup ring is a graded S-Noetherian ring. Finally, we give an example of a graded S-Noetherian ring which is not an S-Noetherian ring.

Original language	English
Article number	1532
Journal	Mathematics
Volume	8
Issue number	9
DOIs	https://doi.org/10.3390/math8091532
State	Published - Sep 2020

Keywords

Cohen type theorem
Graded S-Noetherian ring
S-finite algebra
S-Noetherian ring

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10.3390/math8091532

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title = "When are graded rings graded S-Noetherian rings",

abstract = "Let G be a commutative monoid, R = ⊕α∈Γ Rα a Γ-graded ring and S a multiplicative subset of R0. We define R to be a graded S-Noetherian ring if every homogeneous ideal of R is S-finite. In this paper, we characterize when the ring R is a graded S-Noetherian ring. As a special case, we also determine when the semigroup ring is a graded S-Noetherian ring. Finally, we give an example of a graded S-Noetherian ring which is not an S-Noetherian ring.",

keywords = "Cohen type theorem, Graded S-Noetherian ring, S-finite algebra, S-Noetherian ring",

author = "Kim, {Dong Kyu} and Lim, {Jung Wook}",

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AU - Kim, Dong Kyu

AU - Lim, Jung Wook

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N2 - Let G be a commutative monoid, R = ⊕α∈Γ Rα a Γ-graded ring and S a multiplicative subset of R0. We define R to be a graded S-Noetherian ring if every homogeneous ideal of R is S-finite. In this paper, we characterize when the ring R is a graded S-Noetherian ring. As a special case, we also determine when the semigroup ring is a graded S-Noetherian ring. Finally, we give an example of a graded S-Noetherian ring which is not an S-Noetherian ring.

AB - Let G be a commutative monoid, R = ⊕α∈Γ Rα a Γ-graded ring and S a multiplicative subset of R0. We define R to be a graded S-Noetherian ring if every homogeneous ideal of R is S-finite. In this paper, we characterize when the ring R is a graded S-Noetherian ring. As a special case, we also determine when the semigroup ring is a graded S-Noetherian ring. Finally, we give an example of a graded S-Noetherian ring which is not an S-Noetherian ring.

KW - Cohen type theorem

KW - Graded S-Noetherian ring

KW - S-finite algebra

KW - S-Noetherian ring

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VL - 8

JO - Mathematics

JF - Mathematics

IS - 9

M1 - 1532

ER -

When are graded rings graded S-Noetherian rings

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Keywords

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