Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Regularity conditions in nonnoetherian rings


Author: T. Kabele
Journal: Trans. Amer. Math. Soc. 155 (1971), 363-374
MSC: Primary 13.95
MathSciNet review: 0274439
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We show that properties of $ R$-sequences and the Koszul complex which hold for noetherian local rings do not hold for nonnoetherian local rings. For example, we construct a local ring with finitely generated maximal ideal such that $ {\text{hd} _R}M < \infty $ but $ M$ is not generated by an $ R$-sequence. In fact, every element of $ M - {M^2}$ is a zero divisor. Generalizing a result of Dieudonné, we show that even in local (nonnoetherian) integral domains a permutation of an $ R$-sequence is not necessarily an $ R$-sequence.


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


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 13.95

Retrieve articles in all journals with MSC: 13.95


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1971-0274439-8
PII: S 0002-9947(1971)0274439-8
Keywords: Nonnoetherian local ring, regular sequence, quasi-regular sequence, Koszul complex
Article copyright: © Copyright 1971 American Mathematical Society