Some criteria for regular and Gorenstein local rings via syzygy modules

DOI10.1142/S021949881950097XzbMath1411.13016arXiv1611.03263OpenAlexW2594823032MaRDI QIDQ5383876

Dipankar Ghosh

Publication date: 20 June 2019

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.03263

zbMATH Keywords

TorExtcanonical modulesyzygyregularCohen-Macaulaysemidualizing moduleGorensteinminimal multiplicity

Mathematics Subject Classification ID

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Syzygies, resolutions, complexes and commutative rings (13D02) Homological functors on modules of commutative rings (Tor, Ext, etc.) (13D07) Regular local rings (13H05)

Related Items (1)

VANISHING OF (CO)HOMOLOGY OVER DEFORMATIONS OF COHEN-MACAULAY LOCAL RINGS OF MINIMAL MULTIPLICITY

Cites Work

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• Free summands of syzygies of modules over local rings
• Gorenstein rings and modules with high numbers of generators
• On the Hilbert-Samuel function
• On the associated graded ring of a local Cohen-Macaulay ring
• Cohen-Macaulay local rings of maximal embedding dimension
• Support varieties and cohomology over complete intersections
• Characterizations of regular local rings via syzygy modules of the residue field
• Modules with extremal resolutions
• A remarkable property of the (co) syzygy modules of the residue field of a nonregular local ring
• On the growth of the Betti sequence of the canonical module
• Some criteria for the Gorenstein property
• Syzygy modules with semidualizing or G-projective summands
• Local Rings of High Embedding Dimension
• Stable module theory

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