2008/12/19 by Lars Winther Christensen, Christensen, Lars Winther, Hans‐Bjørn Foxby +4
Mathematics · #13-02 #13B10 #13D05 #13H10 #18G25 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras #math.AC #msc:13-02 #msc:13B10 #msc:13D05 #msc:13H10 #msc:18G25
paper · pdf · doi:10.48550/arxiv.0812.3807
A survey of Gorenstein dimensions for modules over commutative rings; 44 pp. Final version, to appear in "Commutative Algebra: Noetherian and non-Noetherian perspectives", Springer-Verlag"
openalex publication_date 2008/12/19 · arxiv created 2010/01/03 · arxiv updated 2010/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.