On the ex1istence of embeddings into modules of finite homological dimensions

Ryo Takahashi, Siamak Yassemi, Yuji Yoshino

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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 ex1tends a result of Auslander and Bridger to rings of higher Krull dimension, and it also improves a result due to Fox1by where the ring is assumed to be CohenMacaulay.

Original languageEnglish
Pages (from-to)2265-2268
Number of pages4
JournalProceedings of the American Mathematical Society
Issue number7
Publication statusPublished - Jul 2010
Externally publishedYes


  • (semi)dualizing module
  • Cohen-Macaulay ring
  • Gorenstein ring
  • Injective dimension
  • Projective dimension

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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