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arXiv · 1511.08012

Characterizations of regular local rings via syzygy modules of the residue field

Dipankar Ghosh·Anjan Gupta·Tony J. Puthenpurakal
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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 $k$ surjects 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. 2015-11-25. Characterizations of regular local rings via syzygy modules of the residue field. https://doi.org/10.1216/jca-2018-10-3-327

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