Transfer of Gorenstein dimensions along ring homomorphisms

Lars Winther Christensen, Sean Sather-Wagstaff

Research output: Contribution to journalArticle

24 Scopus citations

Abstract

A central problem in the theory of Gorenstein dimensions over commutative noetherian rings is to find resolution-free characterizations of the modules for which these invariants are finite. Over local rings, this problem was recently solved for the Gorenstein flat and the Gorenstein projective dimensions; here we give a solution for the Gorenstein injective dimension. Moreover, we establish two formulas for the Gorenstein injective dimension of modules in terms of the depth invariant; they extend formulas for the injective dimension due to Bass and Chouinard.

Original languageEnglish
Pages (from-to)982-989
Number of pages8
JournalJournal of Pure and Applied Algebra
Volume214
Issue number6
DOIs
StatePublished - Jun 2010

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