On maximal ideals of the polynomial ring and some conjectures on Ext-index of rings

DOI10.1142/s0219498824500592OpenAlexW4307713562WikidataQ122911241 ScholiaQ122911241MaRDI QIDQ6067300

Samir Bouchiba

Publication date: 14 December 2023

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219498824500592

zbMATH Keywords

Cohen-Macaulay ringGorenstein ringcomplete intersection ringArtinian ringExt-indexAB ring

Mathematics Subject Classification ID

Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) (14M05) Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) (16E65) Homological dimension and commutative rings (13D05) Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Commutative Noetherian rings and modules (13E05) Regular local rings (13H05) Rings of fractions and localization for commutative rings (13B30)

Cites Work

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• Vanishing of cohomology over Cohen-Macaulay rings
• Absolute integral closure in positive characteristic
• Symmetry in the vanishing of Ext over stably symmetric algebras.
• Algebras that satisfy Auslander's condition on vanishing of cohomology.
• On Ext-indices of ring extensions
• On Jaffard domains
• Vanishing of Ext and Tor over some Cohen-Macaulay local rings
• Nonvanishing cohomology and classes of Gorenstein rings
• Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas. (Séconde partie)
• Absolute Integral Closure
• Remarks on a depth formula, a grade inequality and a conjecture of Auslander
• Symmetry in the vanishing of Ext over Gorenstein rings
• The Converse to a Theorem of Sharp on Gorenstein Modules

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