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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
DOI: https://doi.org/10.1090/S0002-9939-00-05305-3
Published electronically: February 23, 2000
MathSciNet review: 1662273
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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 $\operatorname{E}(M)$.


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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: https://doi.org/10.1090/S0002-9939-00-05305-3
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

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