Almost Cohen-Macaulay and almost regular algebras via almost flat extensions

DOI10.1216/JCA-2012-4-4-445zbMath1263.13026arXiv1003.0265MaRDI QIDQ1947248

Kazuma Shimomoto, Mohsen Asgharzadeh

Publication date: 22 April 2013

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

Full work available at URL: https://arxiv.org/abs/1003.0265

zbMATH Keywords

Cohen-Macaulay algebracoherent ringnon-Noetherian ringalmost zero moduleflat extension, local cohomology modulerings of finite global dimension.

Mathematics Subject Classification ID

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Local cohomology and commutative rings (13D45)

Related Items

Coherence of absolute integral closures, On the n-coherence of the perfect closure of some ring extensions, Unnamed Item, A sufficient condition for the almost Cohen–Macaulayness of the absolute integral closure in dimension 4, An application of the almost purity theorem to the homological conjectures, A VARIANT OF PERFECTOID ABHYANKAR’S LEMMA AND ALMOST COHEN–MACAULAY ALGEBRAS, Unnamed Item

Cites Work

• Unnamed Item
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• F-coherent rings with applications to tight closure theory
• Almost regular sequences and the monomial conjecture
• Non-Noetherian Cohen-Macaulay rings
• Fontaine rings and local cohomology
• Homological properties of the perfect and absolute integral closures of noetherian domains
• On the notion of Cohen-Macaulayness for non-Noetherian rings
• Commutative coherent rings
• Infinite integral extensions and big Cohen-Macaulay algebras
• Finite Tor dimension and failure of coherence in absolute integral closures
• Almost ring theory
• The direct summand conjecture in dimension three.
• Big Cohen-Macaulay algebras in dimension three via Heitmann's theorem.
• Almost Cohen-Macaulay algebras in mixed characteristic via Fontaine rings
• Annihilators of local cohomology in characteristic zero
• Grade of Ideals with Respect to Torsion Theories
• Big Cohen-Macaulay algebras and seeds