Homological dimensions of Burch ideals, submodules and quotients

DOI10.1016/j.jpaa.2024.107647arXiv2212.07418MaRDI QIDQ6198285

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Publication date: 20 March 2024

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2212.07418

zbMATH Keywords

homological dimensionsintegrally closed idealsvanishing of ExtBurch ideals and submodulesvarious local rings

Mathematics Subject Classification ID

Homological dimension and commutative rings (13D05) Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Integral closure of commutative rings and ideals (13B22) Homological functors on modules of commutative rings (Tor, Ext, etc.) (13D07) Other special types of modules and ideals in commutative rings (13C13)

Cites Work

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• Testing for the Gorenstein property
• Integral closedness of complete-intersection ideals
• Complete intersection dimension
• Gorenstein dimensions
• On the ideal case of a conjecture of Auslander and Reiten
• Homological dimensions of rigid modules
• Modules with extremal resolutions
• Burch ideals and Burch rings
• Homological dimensions and Macaulay rings
• On homological dimensions
• Stable module theory
• Vanishing of (co)homology of Burch and related submodules
• Integrally closed \(\mathfrak{m}\)-primary ideals have extremal resolutions

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