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2018 Characterizations of regular local rings via syzygy modules of the residue field
Dipankar Ghosh, Anjan Gupta, Tony J. Puthenpurakal
J. Commut. Algebra 10(3): 327-337 (2018). DOI: 10.1216/JCA-2018-10-3-327

Abstract

Let $R$ be a commutative Noetherian local ring with residue field $k$. We show that, if a finite direct sum of syzygy modules of $k$ maps onto `a semidualizing module' or `a non-zero maximal Cohen-Macaulay module of finite injective dimension,' then $R$ is regular. We also prove that $R$ is regular if and only if some syzygy module of $k$ has a non-zero direct summand of finite injective dimension.

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Dipankar Ghosh. Anjan Gupta. Tony J. Puthenpurakal. "Characterizations of regular local rings via syzygy modules of the residue field." J. Commut. Algebra 10 (3) 327 - 337, 2018. https://doi.org/10.1216/JCA-2018-10-3-327

Information

Published: 2018
First available in Project Euclid: 9 November 2018

zbMATH: 06976318
MathSciNet: MR3874655
Digital Object Identifier: 10.1216/JCA-2018-10-3-327

Subjects:
Primary: 13D02
Secondary: 13D05, 13H05

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

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Vol.10 • No. 3 • 2018
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