Modules and rings satisfying (accr)

Author:

Lu Chin-Pi

Abstract

A module M M over a ring R R is said to satisfy (accr) if the ascending chain of residuals of the form N : B N : B 2 N : B 3 N: B \subseteq N:{B^2} \subseteq N:{B^3} \subseteq \cdots terminates for every submodule N N and every finitely generated ideal B B of R R . A ring satisfies (accr) if it does as a module over itself. This class of rings and modules satisfies various properties of Noetherian rings and modules. For each of the following rings, we investigate a necessary and sufficient condition for the ring to satisfy (accr): polynomial rings, power series rings, valuation rings, and Prüfer domains. We also prove that if R R is a ring satisfying (accr), then every finitely generated R R -module satisfies (accr).

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference13 articles.

1. The Krull intersection theorem. II;Anderson, D. D.;Pacific J. Math.,1976

2. Piecewise Noetherian rings;Beachy, John A.;Comm. Algebra,1984

3. Actualit\'{e}s Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1293;Bourbaki, N.,1961

4. \bysame, Algèbre commutative, Chapters 3 and 4, Hermann, Paris, 1961.

Cited by 12 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. The effect of $S$-accr on intermediate rings between certain pairs of rings;International Electronic Journal of Algebra;2022-04-01

2. On Modules Satisfying S-Noetherian Spectrum Condition;Communications in Mathematics and Statistics;2022-03-29

3. When is (D, K) an S-accr pair?;Arab Journal of Mathematical Sciences;2021-10-29

4. Some results on S-primary ideals of a commutative ring;Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry;2021-04-27

5. Semistar ascending chain conditions over polynomial rings;Ricerche di Matematica;2021-01-23

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3