Maximal orders of global dimension and Krull dimension two

DOI10.1007/BF01388739zbMath0591.16002OpenAlexW2017881838MaRDI QIDQ1074690

Michael Artin

Publication date: 1986

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143340

zbMATH Keywords

global dimensionquotient singularitypower series ringindecomposable Cohen-Macaulay modulesmaximal R-orders

Mathematics Subject Classification ID

Finite rings and finite-dimensional associative algebras (16P10) Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Singularities of surfaces or higher-dimensional varieties (14J17) Commutative Noetherian rings and modules (13E05) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05) Homological dimension in associative algebras (16E10) Chain conditions on annihilators and summands: Goldie-type conditions (16P60) Representation theory of associative rings and algebras (16Gxx)

Related Items

ON THE CENTER OF THE PROJ OFATHREE DIMENSIONAL REGULAR ALGEBRA, Auslander correspondence., Cohen macaulay rings of global dimension two and krull dimension two, Classifications of exact structures and Cohen-Macaulay-finite algebras, Low dimensional orders of finite representation type, Matrix invariants for symmetric groups, The finite dual coalgebra as a quantization of the maximal spectrum, Diophantine undecidability for some function fields of infinite transcendence degree and positive characteristic, On Cohen-Macaulay modules over non-commutative surface singularities, Non-commutative Cohen-Macaulay rings, The ramification divisor of regular tame orders,i, Two-dimensional orders of finite representation type, Quantizable orders over surfaces, A structure theorem for Noetherian P. I. rings with global dimension two, Noncommutative cyclic covers and maximal orders on surfaces, Rational curves and ruled orders on surfaces, Del Pezzo orders on projective surfaces.

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Rings mit only finitely many isomorphism classes of maximal indecomposable Cohen-Macaulay modules
• Non-commutative affine P. I. rings are catenary
• Théoremes de finitude en cohomologie galoisienne
• Rationale Singularitäten komplexer Flächen
• ON THE PURITY OF THE BRANCH LOCUS OF ALGEBRAIC FUNCTIONS
• Homologically Homogeneous Rings
• Construction géométrique de la correspondance de McKay
• Reflexive modules on quotient surface singularities.
• Rational Singularities and Almost Split Sequences
• Tensor Products of Orders
• Maximal Orders over Regular Local Rings of Dimension Two
• Endliche Gruppen I
• Some Elementary Examples of Unirational Varieties Which are Not Rational
• Structure of hereditary orders
• Maximal Orders
• Finite Unitary Reflection Groups
• Reflexive modules over rational double points