Journal of Commutative Algebra

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

Dipankar Ghosh, Anjan Gupta, and Tony J. Puthenpurakal

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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.

Article information

J. Commut. Algebra, Volume 10, Number 3 (2018), 327-337.

First available in Project Euclid: 9 November 2018

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 13D02: Syzygies, resolutions, complexes
Secondary: 13D05: Homological dimension 13H05: Regular local rings

Regular local rings syzygy and cosyzygy modules semi-dualizing modules injective dimension


Ghosh, Dipankar; Gupta, Anjan; Puthenpurakal, Tony J. Characterizations of regular local rings via syzygy modules of the residue field. J. Commut. Algebra 10 (2018), no. 3, 327--337. doi:10.1216/JCA-2018-10-3-327.

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