On nonnil-S-Noetherian rings

Min Jae Kwon; Jung Wook Lim

doi:10.3390/MATH8091428

On nonnil-S-Noetherian rings

Min Jae Kwon, Jung Wook Lim

Kyungpook National University

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

14 Scopus citations

Abstract

Let R be a commutative ring with identity, and let S be a (not necessarily saturated) multiplicative subset of R. We define R to be a nonnil-S-Noetherian ring if each nonnil ideal of R is S-finite. In this paper, we study some properties of nonnil-S-Noetherian rings. More precisely, we investigate nonnil-S-Noetherian rings via the Cohen-type theorem, the flat extension, the faithfully flat extension, the polynomial ring extension, and the power series ring extension.

Original language	English
Article number	1428
Journal	Mathematics
Volume	8
Issue number	9
DOIs	https://doi.org/10.3390/MATH8091428
State	Published - Sep 2020

Keywords

Nonnil-S-Noetherian ring
S-finite ideal
S-Noetherian ring
SFT ring

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10.3390/MATH8091428

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title = "On nonnil-S-Noetherian rings",

abstract = "Let R be a commutative ring with identity, and let S be a (not necessarily saturated) multiplicative subset of R. We define R to be a nonnil-S-Noetherian ring if each nonnil ideal of R is S-finite. In this paper, we study some properties of nonnil-S-Noetherian rings. More precisely, we investigate nonnil-S-Noetherian rings via the Cohen-type theorem, the flat extension, the faithfully flat extension, the polynomial ring extension, and the power series ring extension.",

keywords = "Nonnil-S-Noetherian ring, S-finite ideal, S-Noetherian ring, SFT ring",

author = "Kwon, \{Min Jae\} and Lim, \{Jung Wook\}",

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year = "2020",

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doi = "10.3390/MATH8091428",

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T1 - On nonnil-S-Noetherian rings

AU - Kwon, Min Jae

AU - Lim, Jung Wook

PY - 2020/9

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N2 - Let R be a commutative ring with identity, and let S be a (not necessarily saturated) multiplicative subset of R. We define R to be a nonnil-S-Noetherian ring if each nonnil ideal of R is S-finite. In this paper, we study some properties of nonnil-S-Noetherian rings. More precisely, we investigate nonnil-S-Noetherian rings via the Cohen-type theorem, the flat extension, the faithfully flat extension, the polynomial ring extension, and the power series ring extension.

AB - Let R be a commutative ring with identity, and let S be a (not necessarily saturated) multiplicative subset of R. We define R to be a nonnil-S-Noetherian ring if each nonnil ideal of R is S-finite. In this paper, we study some properties of nonnil-S-Noetherian rings. More precisely, we investigate nonnil-S-Noetherian rings via the Cohen-type theorem, the flat extension, the faithfully flat extension, the polynomial ring extension, and the power series ring extension.

KW - Nonnil-S-Noetherian ring

KW - S-finite ideal

KW - S-Noetherian ring

KW - SFT ring

UR - https://www.scopus.com/pages/publications/85090495451

U2 - 10.3390/MATH8091428

DO - 10.3390/MATH8091428

M3 - Article

AN - SCOPUS:85090495451

SN - 2227-7390

VL - 8

JO - Mathematics

JF - Mathematics

IS - 9

M1 - 1428

ER -

On nonnil-S-Noetherian rings

Abstract

Keywords

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