Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Injective resolutions of Noetherian rings
and cogenerators


Author: Jun-ichi Miyachi
Journal: Proc. Amer. Math. Soc. 128 (2000), 2233-2242
MSC (1991): Primary 16D50, 16D90, 16E10, 18G35; Secondary 16D20, 18E30
Published electronically: February 23, 2000
MathSciNet review: 1662273
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We give new construction of injective resolutions of complexes and bimodules. Applying this construction to an injective resolution of a Noetherian ring, we construct a $\Sigma$-embedding cogenerator for the category of modules of projective dimension $\leq n$. Moreover, for a Noetherian projective $k$-algebra $R$, we show that $R$ satisfies the Auslander condition if and only if the flat dimension of every $R$-module $M$ is equal to or larger than the one of the injective hull $\operatorname{E}(M)$.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 16D50, 16D90, 16E10, 18G35, 16D20, 18E30

Retrieve articles in all journals with MSC (1991): 16D50, 16D90, 16E10, 18G35, 16D20, 18E30


Additional Information

Jun-ichi Miyachi
Affiliation: Department of Mathematics, Tokyo Gakugei University, Koganei-shi, Tokyo 184-8501, Japan
Email: miyachi@u-gakugei.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05305-3
PII: S 0002-9939(00)05305-3
Received by editor(s): June 25, 1998
Received by editor(s) in revised form: September 15, 1998
Published electronically: February 23, 2000
Communicated by: Ken Goodearl
Article copyright: © Copyright 2000 American Mathematical Society