Characterizations of regular local rings via syzygy modules of the residue field

DOI10.1216/JCA-2018-10-3-327zbMath1408.13035arXiv1511.08012OpenAlexW3099002021MaRDI QIDQ1622004

Dipankar Ghosh, Tony Joseph Puthenpurakal, Anjan Kumar Gupta

Publication date: 12 November 2018

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

Full work available at URL: https://arxiv.org/abs/1511.08012

zbMATH Keywords

injective dimensionregular local ringssemi-dualizing modulessyzygy and cosyzygy modules

Mathematics Subject Classification ID

Homological dimension and commutative rings (13D05) Syzygies, resolutions, complexes and commutative rings (13D02) Regular local rings (13H05)

Related Items (6)

Unnamed Item ⋮ Gorenstein rings via homological dimensions, and symmetry in vanishing of Ext and Tate cohomology ⋮ Integrally closed \(\mathfrak{m}\)-primary ideals have extremal resolutions ⋮ Auslander-Reiten conjecture and finite injective dimension of \(\operatorname{Hom}\) ⋮ Some criteria for regular and Gorenstein local rings via syzygy modules ⋮ VANISHING OF (CO)HOMOLOGY OVER DEFORMATIONS OF COHEN-MACAULAY LOCAL RINGS OF MINIMAL MULTIPLICITY

Cites Work

• Modules with extremal resolutions
• A remarkable property of the (co) syzygy modules of the residue field of a nonregular local ring
• Homological dimensions and Macaulay rings
• Syzygy modules with semidualizing or G-projective summands
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
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