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On the existence of embeddings into modules of finite homological dimensions

Let R be a commutative Noetherian local ring. We show that R is Gorenstein if and only if every finitely generated R-module can be embedded in a finitely generated R-module of finite projective dimension. This extends a result of Auslander and Bridger to rings of higher Krull dimension, and it also improves a result due to Foxby where the ring is assumed to be Cohen-Macaulay.

preprint2010arXivOpen access
Ryo TakahashiSiamak YassemiYuji Yoshino
math.ACmath.RA
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Ryo TakahashiSiamak YassemiYuji Yoshino

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