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.
Citation
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
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