On the ex1istence of embeddings into modules of finite homological dimensions

Ryo Takahashi, Siamak Yassemi, Yuji Yoshino

Research output: Contribution to journalArticle

3 Citations (Scopus)

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 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
Volume138
Issue number7
DOIs
Publication statusPublished - Jul 1 2010

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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