Characterizations of regular local rings via syzygy modules of the residue field
D Ghosh, A Gupta, TJ Puthenpurakal - Journal of Commutative Algebra, 2018 - JSTOR
D Ghosh, A Gupta, TJ Puthenpurakal
Journal of Commutative Algebra, 2018•JSTORLet 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.
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.
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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