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arXiv · 0811.4461

On the existence of embeddings into modules of finite homological dimensions

Ryo Takahashi·Siamak Yassemi·Yuji Yoshino
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Abstract

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.

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Ryo Takahashi, Siamak Yassemi, Yuji Yoshino. 2010-04-02. On the existence of embeddings into modules of finite homological dimensions. https://arxiv.org/abs/0811.4461

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