Abstract
Let R be a commutative Noetherian ring. We consider the question of when n-syzygy modules over R are n-torsionfree in the sense of Auslander and Bridger. Our tools include Serre’s condition and certain conditions on the local Gorenstein property of R. Our main result implies the converse of a celebrated theorem of Evans and Griffith.
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Hiroki Matsui was partly supported by JSPS Grant-in-Aid for JSPS Fellows 16J01067. Ryo Takahashi was partly supported by JSPS Grants-in-Aid for Scientific Research 25400038 and 16K05098.
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Matsui, H., Takahashi, R. & Tsuchiya, Y. When are \({\varvec{n}}\)-syzygy modules \({\varvec{n}}\)-torsionfree?. Arch. Math. 108, 351–355 (2017). https://doi.org/10.1007/s00013-017-1020-9
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DOI: https://doi.org/10.1007/s00013-017-1020-9