On the existence of embeddings into modules of finite homological dimensions

Details On the existence of embeddings into modules of finite homological dimensions On the existence of embeddings into modules of finite homological dimensions

2008-11-27

arxiv.org/abs/0811.4461v3

Mathematics

Commutative Algebra

4 pages, final version, to appear in Proc. Amer. Math. Soc

Scientific paper

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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