Coverart for item
The Resource Local algebra, Jean-Pierre Serre ; translated from the French by CheeWhye Chin

Local algebra, Jean-Pierre Serre ; translated from the French by CheeWhye Chin

Label
Local algebra
Title
Local algebra
Statement of responsibility
Jean-Pierre Serre ; translated from the French by CheeWhye Chin
Creator
Subject
Language
  • eng
  • fre
  • eng
Member of
Cataloging source
DLC
http://library.link/vocab/creatorDate
1926-
http://library.link/vocab/creatorName
Serre, Jean-Pierre
Dewey number
516.3/5
Index
index present
LC call number
QA564
LC item number
.S4313 2000
Literary form
non fiction
Nature of contents
bibliography
Series statement
Springer monographs in mathematics,
http://library.link/vocab/subjectName
  • Geometry, Algebraic
  • Local rings
  • Modules (Algebra)
  • Dimension theory (Algebra)
Label
Local algebra, Jean-Pierre Serre ; translated from the French by CheeWhye Chin
Instantiates
Publication
Bibliography note
Includes bibliographical references (pages [123]-126) and indexes
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 4.
  • Noetherian rings and modules
  • 5.
  • Spectrum
  • 6.
  • noetherian case
  • 7.
  • Associated prime ideals
  • 8.
  • Primary decompositions
  • I.
  • II.
  • Tools
  • A.
  • Filtrations and Gradings
  • 1.
  • Filtered rings and modules
  • 2.
  • Topology defined by a filtration
  • 3.
  • Completion of filtered modules
  • Prime Ideals and Localization
  • 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
  • 1.
  • 3.
  • Hilbert polynomial
  • 4.
  • Samuel polynomial
  • III.
  • Dimension Theory
  • A.
  • Dimension of Integral Extensions
  • 1.
  • Definitions
  • Notation and 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
  • 2.
  • 3.
  • Systems of parameters
  • C.
  • Normal Rings
  • 1.
  • Characterization of normal rings
  • 2.
  • Properties of normal rings
  • 3.
  • Integral closure
  • Nakayama's lemma
  • 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
  • 3.
  • 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
  • Localization
  • 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
  • 3.
  • 2.
  • noetherian case
  • 3.
  • local case
  • D.
  • Regular Rings
  • 1.
  • Properties and characterizations of regular local rings
  • 2.
  • Permanence properties of regular local rings
  • Filtration of a Koszul complex
  • 3.
  • Delocalization
  • 4.
  • criterion for normality
  • 5.
  • Regularity in ring extensions.
  • App. I.
  • Minimal Resolutions
  • App. II.
  • Positivity of Higher Euler-Poincare Characteristics
  • 4.
  • App. III.
  • Graded-polynomial Algebras
  • V.
  • Multiplicities
  • A.
  • Multiplicity of a Module
  • 1.
  • group of cycles of a ring
  • 2.
  • Multiplicity of a module
  • depth of a module over a noetherian local ring
  • B.
  • Intersection Multiplicity of Two Modules
  • 1.
  • Reduction to the diagonal
  • 2.
  • Completed tensor products
  • 3.
  • Regular rings of equal characteristic
  • 4.
  • Conjectures
  • B.
  • 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
  • Cohen-Macaulay Modules
  • 3.
  • Basic formulae
  • 4.
  • Proof of theorem 1
  • 5.
  • Rationality of intersections
  • 1.
  • Definition of Cohen-Macaulay modules
Control code
44084015
Dimensions
24 cm
Extent
xiii, 128 pages
Isbn
9783540666417
Isbn Type
(acid-free paper)
Lccn
00032970
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Label
Local algebra, Jean-Pierre Serre ; translated from the French by CheeWhye Chin
Publication
Bibliography note
Includes bibliographical references (pages [123]-126) and indexes
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 4.
  • Noetherian rings and modules
  • 5.
  • Spectrum
  • 6.
  • noetherian case
  • 7.
  • Associated prime ideals
  • 8.
  • Primary decompositions
  • I.
  • II.
  • Tools
  • A.
  • Filtrations and Gradings
  • 1.
  • Filtered rings and modules
  • 2.
  • Topology defined by a filtration
  • 3.
  • Completion of filtered modules
  • Prime Ideals and Localization
  • 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
  • 1.
  • 3.
  • Hilbert polynomial
  • 4.
  • Samuel polynomial
  • III.
  • Dimension Theory
  • A.
  • Dimension of Integral Extensions
  • 1.
  • Definitions
  • Notation and 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
  • 2.
  • 3.
  • Systems of parameters
  • C.
  • Normal Rings
  • 1.
  • Characterization of normal rings
  • 2.
  • Properties of normal rings
  • 3.
  • Integral closure
  • Nakayama's lemma
  • 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
  • 3.
  • 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
  • Localization
  • 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
  • 3.
  • 2.
  • noetherian case
  • 3.
  • local case
  • D.
  • Regular Rings
  • 1.
  • Properties and characterizations of regular local rings
  • 2.
  • Permanence properties of regular local rings
  • Filtration of a Koszul complex
  • 3.
  • Delocalization
  • 4.
  • criterion for normality
  • 5.
  • Regularity in ring extensions.
  • App. I.
  • Minimal Resolutions
  • App. II.
  • Positivity of Higher Euler-Poincare Characteristics
  • 4.
  • App. III.
  • Graded-polynomial Algebras
  • V.
  • Multiplicities
  • A.
  • Multiplicity of a Module
  • 1.
  • group of cycles of a ring
  • 2.
  • Multiplicity of a module
  • depth of a module over a noetherian local ring
  • B.
  • Intersection Multiplicity of Two Modules
  • 1.
  • Reduction to the diagonal
  • 2.
  • Completed tensor products
  • 3.
  • Regular rings of equal characteristic
  • 4.
  • Conjectures
  • B.
  • 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
  • Cohen-Macaulay Modules
  • 3.
  • Basic formulae
  • 4.
  • Proof of theorem 1
  • 5.
  • Rationality of intersections
  • 1.
  • Definition of Cohen-Macaulay modules
Control code
44084015
Dimensions
24 cm
Extent
xiii, 128 pages
Isbn
9783540666417
Isbn Type
(acid-free paper)
Lccn
00032970
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n

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      38.944377 -92.326537
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