Beyond totally reflexive modules and back A survey on gorenstein dimensions

Lars Winther Christensen, Hans Bjorn Foxby, Henrik Holm

Research output: Chapter in Book/Report/Conference proceedingChapter

43 Scopus citations

Abstract

Starting from the notion of totally reflexive modules, we survey the theory of Gorenstein homological dimensions for modules over commutative rings. The account includes the theory's connections with relative homological algebra and with studies of local ring homomorphisms. It ends close to the starting point: with a characterization of Gorenstein rings in terms of total acyclicity of complexes.

Original languageEnglish
Title of host publicationCommutative Algebra
Subtitle of host publicationNoetherian and Non-Noetherian Perspectives
PublisherSpringer New York
Pages101-143
Number of pages43
ISBN (Print)9781441969897
DOIs
StatePublished - 2011

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    Christensen, L. W., Foxby, H. B., & Holm, H. (2011). Beyond totally reflexive modules and back A survey on gorenstein dimensions. In Commutative Algebra: Noetherian and Non-Noetherian Perspectives (pp. 101-143). Springer New York. https://doi.org/10.1007/978-1-4419-6990-3_5