On the splitting of big Cohen-Macaulay modules

DOI10.1016/S0022-4049(98)00002-4zbMath0972.13012MaRDI QIDQ1295530

Phillip Griffith

Publication date: 16 August 1999

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

zbMATH Keywords

big Cohen-Macaulay modulesinfinite syzygiescountably generated modulecyclic hypersurface ringssmall Cohen-Macaulay modules

Mathematics Subject Classification ID

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Singularities in algebraic geometry (14B05) Singularities of surfaces or higher-dimensional varieties (14J17) Extension theory of commutative rings (13B02) Cohen-Macaulay modules (13C14) Étale and flat extensions; Henselization; Artin approximation (13B40)

Related Items

Maps on divisor class groups induced by ring homomorphisms of finite flat dimension, Exact categories, big Cohen-Macaulay modules and finite representation type, Tensor complexes: multilinear free resolutions constructed from higher tensors, The limiting behavior on the restriction of divisor classes to hypersurfaces., FREENESS OF THE SYMBOLIC CONORMAL MODULE AND MAPS OF DIVISOR CLASSES

Cites Work

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• Injective modules over Noetherian rings
• Projective modules
• Einfache Kurvensingularitäten und torsionsfreie Moduln
• Some results in local rings on ramification in low codimension
• Normal extension of regular local rings
• A representation theorem for complete local rings
• The purity of the Frobenius and local cohomology
• Rings mit only finitely many isomorphism classes of maximal indecomposable Cohen-Macaulay modules
• Maximal Cohen-Macaulay modules and representation theory
• The classification of homogeneous Cohen-Macaulay rings of finite representation type
• Cohen-Macaulay modules on hypersurface singularities. II
• Weak purity for Gorenstein rings
• On the structure of Tor. II
• Purity and algebraic compactness for modules
• On the decomposition of modules and generalized left uniserial rings
• Separable algebras over commutative rings
• Critères de platitude et de projectivité. Techniques de platification d'un module. (Criterial of flatness and projectivity. Technics of flatification of a module.)
• On the ubiquity of Gorenstein rings
• Infinite coverings of ideals by cosets with applications to regular sequences and balanced big Cohen–Macaulay modules
• On the Purity of the Branch Locus
• Cohen–Macaulay properties for balanced big Cohen–Macaulay modules
• A Krull-Schmidt Theorem for Infinite Sums of Modules
• Rings of Continuous Functions and Totally Integrally Closed Rings
• Stable module theory
• On the Structure and Ideal Theory of Complete Local Rings
• Algebraic \(K\)-theory