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• catalog alternative "Algèbre locale, multiplicités. English".
• catalog contributor b12188761.
• catalog created "c2000.".
• catalog date "2000".
• catalog date "c2000.".
• catalog dateCopyrighted "c2000.".
• catalog description "3. Filtration of a Koszul complex -- 4. depth of a module over a noetherian local ring -- B. Cohen-Macaulay Modules -- 1. Definition of Cohen-Macaulay modules -- 2. Several characterizations of Cohen-Macaulay modules -- 3. support of a Cohen-Macaulay module -- 4. Prime ideals and completion -- C. Homological Dimension and Noetherian Modules -- 1. homological dimension of a module -- 2. noetherian case -- 3. local case -- D. Regular Rings -- 1. Properties and characterizations of regular local rings -- 2. Permanence properties of regular local rings -- 3. Delocalization -- 4. criterion for normality -- 5. Regularity in ring extensions. App. I. Minimal Resolutions -- App. II. Positivity of Higher Euler-Poincare Characteristics -- App. III. Graded-polynomial Algebras -- V. Multiplicities -- A. Multiplicity of a Module -- 1. group of cycles of a ring -- 2. Multiplicity of a module -- B. Intersection Multiplicity of Two Modules -- 1. Reduction to the diagonal -- 2. Completed tensor products -- 3. Regular rings of equal characteristic -- 4. Conjectures -- 5. Regular rings of unequal characteristic (unramified case) -- 6. Arbitrary regular rings -- C. Connection with Algebraic Geometry -- 1. Tor-formula -- 2. Cycles on a non-singular affine variety -- 3. Basic formulae -- 4. Proof of theorem 1 -- 5. Rationality of intersections.".
• catalog description "I. Prime Ideals and Localization -- 1. Notation and definitions -- 2. Nakayama's lemma -- 3. Localization -- 4. Noetherian rings and modules -- 5. Spectrum -- 6. noetherian case -- 7. Associated prime ideals -- 8. Primary decompositions -- II. Tools -- A. Filtrations and Gradings -- 1. Filtered rings and modules -- 2. Topology defined by a filtration -- 3. Completion of filtered modules -- 4. Graded rings and modules -- 5. Where everything becomes noetherian again -- q-adic filtrations -- B. Hilbert-Samuel Polynomials -- 1. Review on integer-valued polynomials -- 2. Polynomial-like functions -- 3. Hilbert polynomial -- 4. Samuel polynomial -- III. Dimension Theory -- A. Dimension of Integral Extensions -- 1. Definitions -- 2. Cohen-Seidenberg first theorem -- 3. Cohen-Seidenberg second theorem -- B. Dimension in Noetherian Rings -- 1. Dimension of a module -- 2. case of noetherian local rings -- 3. Systems of parameters -- C. Normal Rings -- 1. Characterization of normal rings -- 2. Properties of normal rings -- 3. Integral closure -- D. Polynomial Rings -- 1. Dimension of the ring A[X[subscript 1], ..., X[subscript n]] -- 2. normalization lemma -- 3. Applications. I. Dimension in polynomial algebras -- 4. Applications. II. Integral closure of a finitely generated algebra -- 5. Applications. III. Dimension of an intersection in affine space -- IV. Homological Dimension and Depth -- A. Koszul Complex -- 1. simple case -- 2. Acyclicity and functorial properties of the Koszul complex.".
• catalog description "Includes bibliographical references (p. [123]-126) and indexes.".
• catalog extent "xiii, 128 p. ;".
• catalog identifier "3540666419 (acid-free paper)".
• catalog isPartOf "Springer monographs in mathematics, 1439-7382".
• catalog issued "2000".
• catalog issued "c2000.".
• catalog language "eng fre".
• catalog language "eng".
• catalog publisher "Berlin ; New York : Springer,".
• catalog subject "516.3/5 21".
• catalog subject "Dimension theory (Algebra)".
• catalog subject "Geometry, Algebraic.".
• catalog subject "Local rings.".
• catalog subject "Modules (Algebra)".
• catalog subject "QA564 .S4313 2000".
• catalog tableOfContents "3. Filtration of a Koszul complex -- 4. depth of a module over a noetherian local ring -- B. Cohen-Macaulay Modules -- 1. Definition of Cohen-Macaulay modules -- 2. Several characterizations of Cohen-Macaulay modules -- 3. support of a Cohen-Macaulay module -- 4. Prime ideals and completion -- C. Homological Dimension and Noetherian Modules -- 1. homological dimension of a module -- 2. noetherian case -- 3. local case -- D. Regular Rings -- 1. Properties and characterizations of regular local rings -- 2. Permanence properties of regular local rings -- 3. Delocalization -- 4. criterion for normality -- 5. Regularity in ring extensions. App. I. Minimal Resolutions -- App. II. Positivity of Higher Euler-Poincare Characteristics -- App. III. Graded-polynomial Algebras -- V. Multiplicities -- A. Multiplicity of a Module -- 1. group of cycles of a ring -- 2. Multiplicity of a module -- B. Intersection Multiplicity of Two Modules -- 1. Reduction to the diagonal -- 2. Completed tensor products -- 3. Regular rings of equal characteristic -- 4. Conjectures -- 5. Regular rings of unequal characteristic (unramified case) -- 6. Arbitrary regular rings -- C. Connection with Algebraic Geometry -- 1. Tor-formula -- 2. Cycles on a non-singular affine variety -- 3. Basic formulae -- 4. Proof of theorem 1 -- 5. Rationality of intersections.".
• catalog tableOfContents "I. Prime Ideals and Localization -- 1. Notation and definitions -- 2. Nakayama's lemma -- 3. Localization -- 4. Noetherian rings and modules -- 5. Spectrum -- 6. noetherian case -- 7. Associated prime ideals -- 8. Primary decompositions -- II. Tools -- A. Filtrations and Gradings -- 1. Filtered rings and modules -- 2. Topology defined by a filtration -- 3. Completion of filtered modules -- 4. Graded rings and modules -- 5. Where everything becomes noetherian again -- q-adic filtrations -- B. Hilbert-Samuel Polynomials -- 1. Review on integer-valued polynomials -- 2. Polynomial-like functions -- 3. Hilbert polynomial -- 4. Samuel polynomial -- III. Dimension Theory -- A. Dimension of Integral Extensions -- 1. Definitions -- 2. Cohen-Seidenberg first theorem -- 3. Cohen-Seidenberg second theorem -- B. Dimension in Noetherian Rings -- 1. Dimension of a module -- 2. case of noetherian local rings -- 3. Systems of parameters -- C. Normal Rings -- 1. Characterization of normal rings -- 2. Properties of normal rings -- 3. Integral closure -- D. Polynomial Rings -- 1. Dimension of the ring A[X[subscript 1], ..., X[subscript n]] -- 2. normalization lemma -- 3. Applications. I. Dimension in polynomial algebras -- 4. Applications. II. Integral closure of a finitely generated algebra -- 5. Applications. III. Dimension of an intersection in affine space -- IV. Homological Dimension and Depth -- A. Koszul Complex -- 1. simple case -- 2. Acyclicity and functorial properties of the Koszul complex.".
• catalog title "Algèbre locale, multiplicités. English".
• catalog title "Local algebra / Jean-Pierre Serre ; translated from the French by CheeWhye Chin.".
• catalog type "text".