Abstract
We refine a well-known theorem of Auslander and Reiten about the extension closedness of nth 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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Presented by Peter Littelmann.
The first author was partly supported by JSPS Grant-in-Aid for Scientific Research (C) 25400051. The second author was partly supported by JSPS Grant-in-Aid for Scientific Research (C) 25400038.
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Goto, S., Takahashi, R. Extension Closedness of Syzygies and Local Gorensteinness of Commutative Rings. Algebr Represent Theor 19, 511–521 (2016). https://doi.org/10.1007/s10468-015-9585-0
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DOI: https://doi.org/10.1007/s10468-015-9585-0