Kyoto Journal of Mathematics
- Kyoto J. Math.
- Volume 58, Number 3 (2018), 639-669.
Homological dimensions of rigid modules
We obtain various characterizations of commutative Noetherian local rings in terms of homological dimensions of certain finitely generated modules. Our argument has a series of consequences in different directions. For example, we establish that is Gorenstein if the Gorenstein injective dimension of the maximal ideal of is finite. Moreover, we prove that must be regular if a single vanishes for some integrally closed -primary ideals and of and for some positive integer .
Kyoto J. Math., Volume 58, Number 3 (2018), 639-669.
Received: 19 February 2016
Revised: 8 December 2016
Accepted: 9 December 2016
First available in Project Euclid: 19 June 2018
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Zargar, Majid Rahro; Celikbas, Olgur; Gheibi, Mohsen; Sadeghi, Arash. Homological dimensions of rigid modules. Kyoto J. Math. 58 (2018), no. 3, 639--669. doi:10.1215/21562261-2017-0033. https://projecteuclid.org/euclid.kjm/1529373739