Illinois Journal of Mathematics

Modules of G-dimension zero over local rings of depth two

Ryo Takahashi

Full-text: Open access


Let $R$ be a commutative noetherian local ring. Denote by $\mod R$ the category of finitely generated $R$-modules, and by ${\mathcal G} (R)$ the full subcategory of $\mod R$ consisting of all $R$-modules of G-dimension zero. Suppose that $R$ is henselian and non-Gorenstein, and that there is a non-free $R$-module in ${\mathcal G} (R)$. Then it is known that ${\mathcal G} (R)$ is not contravariantly finite in $\mod R$ if $R$ has depth at most one. In this paper, we prove that the same statement holds if $R$ has depth two.

Article information

Illinois J. Math., Volume 48, Number 3 (2004), 945-952.

First available in Project Euclid: 13 November 2009

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 13D05: Homological dimension


Takahashi, Ryo. Modules of G-dimension zero over local rings of depth two. Illinois J. Math. 48 (2004), no. 3, 945--952. doi:10.1215/ijm/1258131062.

Export citation