Totally reflexive modules over rings that are close to Gorenstein

DOI10.1016/j.jalgebra.2018.09.012zbMath1453.13003arXiv1705.05714OpenAlexW2962897198MaRDI QIDQ2219010

Andrew R. Kustin, Adela Vraciu

Publication date: 18 January 2021

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.05714

zbMATH Keywords

canonical moduletotally reflexive modulestest modulesGorenstein colengthG-regular local ringhigher matrix factorizationsummands of syzygiesteter ring

Mathematics Subject Classification ID

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Graded rings (13A02) Syzygies, resolutions, complexes and commutative rings (13D02) Homological dimension (category-theoretic aspects) (18G20)

Related Items

On reflexive and 𝐼-Ulrich modules over curve singularities ⋮ Existence and Constructions of Totally Reflexive Modules ⋮ Test modules, weakly regular homomorphisms and complete intersection dimension ⋮ Burch index, summands of syzygies and linearity in resolutions ⋮ Burch ideals and Burch rings ⋮ Totally reflexive modules over connected sums with \(\mathfrak{m}^3 =0\)

Uses Software

• Macaulay2

Cites Work

• Unnamed Item
• Unnamed Item
• Testing for the Gorenstein property
• Minimal free resolutions over complete intersections
• Modules that detect finite homological dimensions
• Poincaré series of modules over compressed Gorenstein local rings
• On the ubiquity of Gorenstein rings
• Éléments de géométrie algébrique. III: Étude cohomologique des faisceaux cohérents. (Séconde partie). Rédigé avec la colloboration de J. Dieudonné
• ABSOLUTE, RELATIVE, AND TATE COHOMOLOGY OF MODULES OF FINITE GORENSTEIN DIMENSION
• A family of complexes associated to an almost alternating map, with applications to residual intersections
• On G-Regular Local Rings
• ON TEST MODULES FOR FLAT DIMENSION
• Stable module theory