Correspondence between trace ideals and birational extensions with application to the analysis of the Gorenstein property of rings

DOI10.1016/j.jpaa.2019.06.008zbMath1432.13018arXiv1802.08409OpenAlexW2963577848MaRDI QIDQ2318413

Shiro Goto, Ryotaro Isobe, Shinya Kumashiro

Publication date: 15 August 2019

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

Full work available at URL: https://arxiv.org/abs/1802.08409

zbMATH Keywords

Cohen-Macaulay ringGorenstein ringstable ringstable idealtrace idealtrace module

Mathematics Subject Classification ID

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Multiplicity theory and related topics (13H15) Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics (13A30)

Related Items (11)

Trace ideals of semidualizing modules and two generalizations of nearly Gorenstein rings ⋮ On reflexive and 𝐼-Ulrich modules over curve singularities ⋮ The trace property in preenveloping classes ⋮ Ulrich ideals and 2-AGL rings ⋮ The reduction number of canonical ideals ⋮ When are trace ideals finite? ⋮ The tiny trace ideals of the canonical modules in Cohen-Macaulay rings of dimension one ⋮ Reflexive modules over the endomorphism algebras of reflexive trace ideals ⋮ On the set of trace ideals of a Noetherian ring ⋮ Trace ideals of canonical modules, annihilators of Ext modules, and classes of rings close to being Gorenstein ⋮ Almost Gorenstein rings arising from fiber products

Cites Work

• Almost Gorenstein rings
• Bounds for the first Hilbert coefficients of \(\mathfrak{m}\)-primary ideals
• Trace ideals and centers of endomorphism rings of modules over commutative rings
• On semi-hereditary rings
• Cohen-Macaulay local rings of maximal embedding dimension
• Stable rings
• Almost Gorenstein rings - towards a theory of higher dimension
• The trace of the canonical module
• Der kanonische Modul eines Cohen-Macaulay-Rings. (The canonical moduls of a Cohen-Macaulay-ring)
• Self-injective group algebras
• On the ubiquity of Gorenstein rings
• Good ideals in Gorenstein local rings
• Trace Ideals and the Gorenstein Property
• Rings whose ideals are isomorphic to trace ideals
• Stable Ideals and Arf Rings
• On Regular Rings

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