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arXiv · 1502.06653

Extension closedness of syzygies and local Gorensteinness of commutative rings

Shiro Goto·Ryo Takahashi
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Abstract

We refine a well-known theorem of Auslander and Reiten about the extension closedness of n-th syzygies over noether algebras. Applying it, we obtain the converse of a celebrated theorem of Evans and Griffith on Serre's condition (S_n) and the local Gorensteiness of a commutative ring in height less than n. This especially extends a recent result of Araya and Iima concerning a Cohen-Macaulay local ring with canonical module to an arbitrary local ring.

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Shiro Goto, Ryo Takahashi. 2015-02-23. Extension closedness of syzygies and local Gorensteinness of commutative rings. https://arxiv.org/abs/1502.06653

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