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 -embedding cogenerator for the category of modules of projective dimension . Moreover, for a Noetherian projective -algebra , we show that satisfies the Auslander condition if and only if the flat dimension of every -module is equal to or larger than the one of the injective hull .

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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