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Paper   IPM / M / 11326
School of Mathematics
  Title:   On existence of embeddings into modules of finite homological dimensions
  Author(s):  S. Yassemi (Joint with R. Takahashi and Y. Yoshino)
  Status:   Published
  Journal: Proc. Amer. Math. Soc.
  Vol.:  138
  Year:  2010
  Pages:   2265-2268
  Supported by:  IPM
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 also improves a result due to Foxby where the ring is assumed to be Cohen-Macaulay.

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