Canonical filtrations of Gorenstein injective modules
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- by Edgar E. Enochs and Zhaoyong Huang PDF
- Proc. Amer. Math. Soc. 139 (2011), 2415-2421 Request permission
Abstract:
The principle “Every result in classical homological algebra should have a counterpart in Gorenstein homological algebra” was given by Henrik Holm. There is a remarkable body of evidence supporting this claim. Perhaps one of the most glaring exceptions is provided by the fact that tensor products of Gorenstein projective modules need not be Gorenstein projective, even over Gorenstein rings. So perhaps it is surprising that tensor products of Gorenstein injective modules over Gorenstein rings of finite Krull dimension are Gorenstein injective.
Our main result is in support of the principle. Over commutative, noetherian rings injective modules have direct sum decompositions into indecomposable modules. We will show that Gorenstein injective modules over Gorenstein rings of finite Krull dimension have filtrations analogous to those provided by these decompositions. This result will then provide us with the tools to prove that all tensor products of Gorenstein injective modules over these rings are Gorenstein injective.
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Additional Information
- Edgar E. Enochs
- Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506
- Email: enochs@ms.uky.edu
- Zhaoyong Huang
- Affiliation: Department of Mathematics, Nanjing University, Nanjing 210093, Jiangsu Province, People’s Republic of China
- Email: huangzy@nju.edu.cn
- Received by editor(s): August 7, 2009
- Received by editor(s) in revised form: July 5, 2010
- Published electronically: December 9, 2010
- Communicated by: Bernd Ulrich
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 2415-2421
- MSC (2010): Primary 13D07, 16E30
- DOI: https://doi.org/10.1090/S0002-9939-2010-10686-X
- MathSciNet review: 2784806