Reduction of the small Cohen-Macaulay conjecture to excellent unique factorization domains

DOI10.1007/s00013-017-1103-7zbMath1401.13046OpenAlexW2757813072WikidataQ123336455 ScholiaQ123336455MaRDI QIDQ1674883

Ehsan Tavanfar

Publication date: 26 October 2017

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00013-017-1103-7

zbMATH Keywords

linkageunique factorization domainsquasi-Gorenstein ringssmall Cohen-Macaulay conjecture

Mathematics Subject Classification ID

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Linkage, complete intersections and determinantal ideals (13C40) Homological conjectures (intersection theorems) in commutative ring theory (13D22) Cohen-Macaulay modules (13C14)

Related Items (5)

Annihilators of Koszul homologies and almost complete intersections ⋮ A sufficient condition for the almost Cohen–Macaulayness of the absolute integral closure in dimension 4 ⋮ Remarks on the small Cohen-Macaulay conjecture and new instances of maximal Cohen-Macaulay modules ⋮ A study of quasi-Gorenstein rings. II: Deformation of quasi-Gorenstein property ⋮ Reductions towards a characteristic free proof of the Canonical Element Theorem

Cites Work

• Gorenstein rings as specializations of unique factorization domains
• Some basic results on canonical modules
• On the endomorphism ring of the canonical module
• On the symmetric and Rees algebra of an ideal generated by a d-sequence
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• Homology of local flat extensions and complete intersection defects
• A study of quasi-Gorenstein rings
• The direct factor conjecture
• Homological conjectures, old and new
• Criteria for equality of ordinary and symbolic powers of primes
• Residual intersections and the annihilator of Koszul homologies
• Hochster’s small MCM conjecture for three-dimensional weakly F-split rings
• Divisor Class Groups and Deformations
• Characterization of Completions of Unique Factorization Domains
• On the Factoriality of Local Rings of Small Embedding Codimension
• A CONSTRUCTION OF QUASI-GORENSTEIN RINGS
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