Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Modules and rings satisfying (accr)

Author: Chin-Pi Lu
Journal: Proc. Amer. Math. Soc. 117 (1993), 5-10
MSC: Primary 13E05; Secondary 13C05, 13F05, 13J10
MathSciNet review: 1104398
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A module $ M$ over a ring $ R$ is said to satisfy (accr) if the ascending chain of residuals of the form $ N: B \subseteq N:{B^2} \subseteq N:{B^3} \subseteq \cdots $ terminates for every submodule $ N$ and every finitely generated ideal $ B$ of $ 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$ is a ring satisfying (accr), then every finitely generated $ R$-module satisfies (accr).

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 13E05, 13C05, 13F05, 13J10

Retrieve articles in all journals with MSC: 13E05, 13C05, 13F05, 13J10

Additional Information

PII: S 0002-9939(1993)1104398-7
Keywords: (accr), Laskerian ring, valuation ring, Prüfer domain
Article copyright: © Copyright 1993 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia