On the ex1istence of embeddings into modules of finite homological dimensions

Ryo Takahashi; Siamak Yassemi; Yuji Yoshino

doi:10.1090/S0002-9939-10-10323-2

On the ex₁istence of embeddings into modules of finite homological dimensions

Ryo Takahashi, Siamak Yassemi, Yuji Yoshino

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	2265-2268
Number of pages	4
Journal	Proceedings of the American Mathematical Society
Volume	138
Issue number	7
DOIs	https://doi.org/10.1090/S0002-9939-10-10323-2
Publication status	Published - Jul 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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AU - Yoshino, Yuji

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KW - Projective dimension

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