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1.

図書

図書
Jean-Pierre Serre
出版情報: Paris : Société mathématique de France, 2001  vi, 259 p. ; 25 cm
シリーズ名: Documents mathématiques ; 1
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2.

図書

図書
éditée Pierre Colmez, Jean-Pierre Serre
出版情報: Paris : Société mathématique de France, 2001  x, 288 p. ; 25 cm
シリーズ名: Documents mathématiques ; 2
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3.

図書

図書
Jean-Pierre Serre ; translated from the French by Patrick Ion
出版情報: Berlin ; Tokyo : Springer, 2002  x, 210 p. ; 25 cm
シリーズ名: Springer monographs in mathematics
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4.

図書

図書
ジャン-ピエール・セール著 ; 鈴木治郎訳
出版情報: 東京 : ピアソン・エデュケーション, 1999.12  xiv, 156p ; 21cm
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5.

図書

図書
Jean-Pierre Serre ; translated from the French by Chee Whye Chin
出版情報: Berlin : Springer, 2000  xiii, 128 p. ; 24 cm
シリーズ名: Springer monographs in mathematics
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目次情報: 続きを見る
Preface
Contents
Introduction
Prime Ideals and Localization / I:
Notation and definitions /  1:
Nakayama's lemma /  2:
Localization /  3:
Noetherian rings and modules /  4:
Spectrum /  5:
The noetherian case /  6:
Associated prime ideals /  7:
Primary decompositions /  8:
Tools / II:
Filtrations and Gradings / A:
Filtered rings and modules
Topology defined by a filtration
Completion of filtered modules
Graded rings and modules
Where everything becomes noetherian again - <$>\mathfr {q}<$> -adic filtrations
Hilbert-Samuel Polynomials / B:
Review on integer-valued polynomials
Polynomial-like functions
The Hilbert polynomial
The Samuel polynomial
Dimension Theory / III:
Dimension of Integral Extensions
Definitions
Cohen-Seidenberg first theorem
Cohen-Seidenberg second theorem
Dimension in Noetherian Rings
Dimension of a module
The case of noetherian local rings
Systems of parameters
Normal Rings / C:
Characterization of normal rings
Properties of normal rings
Integral closure
Polynomial Rings / D:
Dimension of the ring A[X1, ..., Xn]
The normalization lemma
Applications. I. Dimension in polynomial algebras
Applications. II. Integral closure of a finitely generated algebra
Applications. III. Dimension of an intersection in affine space
Homological Dimension and Depth / IV:
The Koszul Complex
The simple case
Acyclicity and functorial properties of the Koszul complex
Filtration of a Koszul complex
The depth of a module over a noetherian local ring
Cohen-Macaulay Modules
Definition of Cohen-Macaulay modules
Several characterizations of Cohen-Macaulay modules
The support of a Cohen-Macaulay module
Prime ideals and completion
Homological Dimension and Noetherian Modules
The homological dimension of a module
The local case
Regular Rings
Properties and characterizations of regular local rings
Permanence properties of regular local rings
Delocalization
A criterion for normality
Regularity in ring extensions
Minimal Resolutions / Appendix I:
Definition of minimal resolutions
Application
The case of the Koszul complex
Positivity of Higher Euler-Poincare Characteristics / Appendix II:
Graded-polynomial Algebras / Appendix III:
Notation
Graded-polynomial algebras
A characterization of graded-polynomial algebras
Ring extensions
Application: the Shephard-Todd theorem
Multiplicities / V:
Multiplicity of a Module
The group of cycles of a ring
Multiplicity of a module
Intersection Multiplicity of Two Modules
Reduction to the diagonal
Completed tensor products
Regular rings of equal characteristic
Conjectures
Regular rings of unequal characteristic (unramified case)
Arbitrary regular rings
Connection with Algebraic Geometry
Tor-formula
Cycles on a non-singular affine variety
Basic formulae
Proof of theorem 1
Rationality of intersections
Direct images
Pull-backs
Extensions of intersection theory
Bibliography
Index
Index of Notation
Preface
Contents
Introduction
6.

図書

図書
Jean-Pierre Serre ; translated from the French by G.A. Jones
出版情報: New York : Springer, 2001  ix, 74 p. ; 25 cm
シリーズ名: Springer monographs in mathematics
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Nilpotent Lie Algebras and Solvable Lie Algebras
Semisimple Lie Algebras (General Theorems)
Cartan Subalgebras
The Algebra sl2 and Its Representations
Root Systems
Structure of Semisimple Lie Algebras
Linear Representations of Semisimple Lie Algebras
Complex Groups and Compact groups
Bibliography
Index
Nilpotent Lie Algebras and Solvable Lie Algebras
Semisimple Lie Algebras (General Theorems)
Cartan Subalgebras
7.

図書

図書
edited by Jean-Pierre Serre and Goro Shimura ; with the cooperation of the editors of the American Journal of Mathematics
出版情報: Baltimore ; London : Johns Hopkins University Press, 1983  594p ; 24cm
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8.

図書

図書
Jean-Pierre Serre ; translated from the French by John Stillwell
出版情報: Berlin ; New York : Springer-Verlag, 1980  ix, 142 p. ; 25 cm
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9.

図書

図書
Jean-Pierre Serre
出版情報: Paris : Hermann, 1962  243 p. ; 24 cm
シリーズ名: Publications de l'Institut de mathématique de l'Université de Nancago ; 8
Actualités scientifiques et industrielles ; 1296
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10.

図書

図書
Jean-Pierre Serre
出版情報: New York ; Tokyo : W.A. Benjamin, 1965  1 v. (various pagings) ; 28 cm
シリーズ名: Mathematics lecture note series
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