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1.

図書

図書
Serge Lang
出版情報: New York ; Berlin : Springer-Verlag, c1987  xi, 326 p. ; 25 cm
シリーズ名: Graduate texts in mathematics ; 112
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General Theory
Complex Multiplication Elliptic Curves with Singular Invariants
Elliptic Curves with Non-integral Invariants
Theta Functions and Kronecker limit Formula
Bibliography
Index
General Theory
Complex Multiplication Elliptic Curves with Singular Invariants
Elliptic Curves with Non-integral Invariants
2.

図書

図書
Serge Lang
出版情報: Berlin ; New York : Springer-Verlag, 1978  xi, 261 p. ; 25 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; Bd. 231
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3.

図書

図書
William Fulton, Serge Lang
出版情報: New York : Springer-Verlag, c1985  x, 203 p. ; 25 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 277
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4.

図書

図書
Serge Lang
出版情報: New York : Springer-Verlag, c1987  viii, 271 p. ; 25 cm
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5.

図書

図書
Serge Lang
出版情報: Reading, Mass. : Addison-Wesley Pub. Co, 1972  ix, 230 p. ; 24 cm
シリーズ名: Addison-Wesley series in mathematics ; 4166
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6.

図書

図書
Serge Lang
出版情報: Reading, Mass. : Addison-Wesley Pub. Co., c1968-1969  2 v. ; 24 cm
シリーズ名: Addison-Wesley series in mathematics
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7.

図書

図書
Serge Lang
出版情報: New York ; Berlin : Springer-Verlag, c1983  viii, 184 p. ; 25 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 255
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8.

図書

図書
Serge Lang
出版情報: New York ; Tokyo : Springer-Verlag, c1987  ix, 256 p. ; 25 cm
シリーズ名: Undergraduate texts in mathematics
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目次情報: 続きを見る
Foreword
The Integers
Groups
Rings
Polynomials
Vector Spaces and Modules
Some Linear Groups
Field Theory
Finite Fields
The Real and Complex Numbers
Sets
Appendix
Index
Foreword
The Integers
Groups
9.

図書

図書
Serge Lang
出版情報: New York ; Tokyo : Springer-Verlag, c1987  xii, 503, 91, 4 p. ; 25 cm
シリーズ名: Undergraduate texts in mathematics
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Basic Material / I:
Vectors / 1:
Differentiation of Vectors / 2:
Functions of Several Variables / 3:
The Chain Rule and the Gradient / 4:
Maxima, Minima, and Taylor's Formula / II:
Maximum and Minimum / 5:
Higher Derivatives / 6:
Curve Integrals and Double Integrals / III:
Potential Functions / 7:
Curve Integrals / 8:
Double Integrals / 9:
Green's Theorem / 10:
Triple and Surface Integrals / IV:
Triple Integrals / 12:
Mappings, Inverse Mappings, and Change of Variables Formula / V:
Matrices / 13:
Linear Mappings / 14:
Determinants / 15:
Applications to Functions of Several Variables / 16:
The Change of Variables Formula / 17:
Appendix: Fourier Series
Basic Material / I:
Vectors / 1:
Differentiation of Vectors / 2:
10.

図書

図書
Serge Lang
出版情報: Reading, Mass. : Addison-Wesley Pub. Co., c1977  xi, 321 p. ; 24 cm
シリーズ名: Addison-Wesley series in mathematics
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11.

図書

図書
Serge Lang
出版情報: Reading ; Mass : Addison-Wesley, 1969,c1971,1972  xi, 400 p. ; 24 cm
シリーズ名: Addison-Wesley series in mathematics
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12.

図書

図書
Serge Lang
出版情報: New York : Springer, c2002  xv, 914 p. ; 25 cm
シリーズ名: Graduate texts in mathematics ; 211
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目次情報: 続きを見る
The Basic Objects of Algebra / Part 1:
Groups / Chapter I:
Monoids / 1.:
Normal subgroups / 2.:
Cyclic groups / 4.:
Operations of a group on a set / 5.:
Sylow subgroups / 6.:
Direct sums and free abelian groups / 7.:
Finitely generated abelian groups / 8.:
The dual group / 9.:
Inverse limit and completion / 10.:
Categories and functors / 11.:
Free groups / 12.:
Rings / Chapter II:
Rings and homomorphisms
Commutative rings
Polynomials and group rings
Localization
Principal and factorial rings
Modules / Chapter III:
Basic definitions
The group of homomorphisms
Direct products and sums of modules
Free modules
Vector spaces
The dual space and dual module
Modules over principal rings
Euler-Poincare maps
The snake lemma
Direct and inverse limits
Polynomials / Chapter IV:
Basic properties for polynomials in one variable
Polynomials over a factorial ring
Criteria for irreducibility
Hilbert's theorem
Partial fractions
Symmetric polynomials
Mason-Stothers theorem and the abc conjecture
The resultant
Power series
Algebraic Equations / Part 2:
Algebraic Extensions / Chapter V:
Finite and algebraic extensions
Algebraic closure
Splitting fields and normal extensions
Separable extensions
Finite fields
Inseparable extensions
Galois Theory / Chapter VI:
Galois extensions
Examples and applications
Roots of unity
Linear independence of characters
The norm and trace
Cyclic extensions
Solvable and radical extensions
Abelian Kummer theory
The equation X[superscript n] - a = 0
Galois cohomology
Non-abelian Kummer extensions
Algebraic independence of homomorphisms
The normal basis theorem / 13.:
Infinite Galois extensions / 14.:
The modular connection / 15.:
Extensions of Rings / Chapter VII:
Integral ring extensions
Integral Galois extensions
Extension of homomorphisms
Transcendental Extensions / Chapter VIII:
Transcendence bases
Noether normalization theorem
Linearly disjoint extensions
Separable and regular extensions
Derivations
Algebraic Spaces / Chapter IX:
Hilbert's Nullstellensatz
Algebraic sets, spaces and varieties
Projections and elimination
Resultant systems
Spec of a ring
Noetherian Rings and Modules / Chapter X:
Basic criteria
Associated primes
Primary decomposition
Nakayama's lemma
Filtered and graded modules
The Hilbert polynomial
Indecomposable modules
Real Fields / Chapter XI:
Ordered fields
Real fields
Real zeros and homomorphisms
Absolute Values / Chapter XII:
Definitions, dependence, and independence
Completions
Finite extensions
Valuations
Completions and valuations
Discrete valuations
Zeros of polynomials in complete fields
Linear Algebra and Representations / Part 3:
Matrices and Linear Maps / Chapter XIII:
Matrices
The rank of a matrix
Matrices and linear maps
Determinants
Duality
Matrices and bilinear forms
Sesquilinear duality
The simplicity of SL[subscript 2](F)/[plus or minus]1
The group SL[subscript n](F), n [greater than or equal] 3
Representation of One Endomorphism / Chapter XIV:
Representations
Decomposition over one endomorphism
The characteristic polynomial
Structure of Bilinear Forms / Chapter XV:
Preliminaries, orthogonal sums
Quadratic maps
Symmetric forms, orthogonal bases
Symmetric forms over ordered fields
Hermitian forms
The spectral theorem (hermitian case)
The spectral theorem (symmetric case)
Alternating forms
The Pfaffian
Witt's theorem
The Witt group
The Tensor Product / Chapter XVI:
Tensor product
Basic properties
Flat modules
Extension of the base
Some functorial isomorphisms
Tensor product of algebras
The tensor algebra of a module
Symmetric products
Semisimplicity / Chapter XVII:
Matrices and linear maps over non-commutative rings
Conditions defining semisimplicity
The density theorem
Semisimple rings
Simple rings
The Jacobson radical, base change, and tensor products
Balanced modules
Representations of Finite Groups / Chapter XVIII:
Representations and semisimplicity
Characters
1-dimensional representations
The space of class functions
Orthogonality relations
Induced characters
Induced representations
Positive decomposition of the regular character
Supersolvable groups
Brauer's theorem
Field of definition of a representation
Example: GL[subscript 2] over a finite field
The Alternating Product / Chapter XIX:
Definition and basic properties
Fitting ideals
Universal derivations and the de Rham complex
The Clifford algebra
Homological Algebra / Part 4:
General Homology Theory / Chapter XX:
Complexes
Homology sequence
Euler characteristic and the Grothendieck group
Injective modules
Homotopies of morphisms of complexes
Derived functors
Delta-functors
Bifunctors
Spectral sequences
Finite Free Resolutions / Chapter XXI:
Special complexes
Finite free resolutions
Unimodular polynomial vectors
The Koszul complex
The Transcendence of e and [Pi] / Appendix 1:
Some Set Theory / Appendix 2:
Bibliography
Index
The Basic Objects of Algebra / Part 1:
Groups / Chapter I:
Monoids / 1.:
13.

図書

図書
Serge Lang
出版情報: New York : Interscience Publishers, c1962  x, 170 p. ; 24 cm
シリーズ名: Interscience tracts in pure and applied mathematics ; no. 11
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14.

図書

図書
Serge Lang
出版情報: New York : Springer-Verlag, c1987  ix, 285 p. ; 25 cm
シリーズ名: Undergraduate texts in mathematics
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目次情報: 続きを見る
Vector Spaces / 1:
Matrices / 2:
Linear Mappings / 3:
Linear Maps and Matrices / 4:
Scalar Products and Orthogonality / 5:
Determinants / 6:
Symmetric, Hermitian, and Unitary Operators / 7:
Eigenvectors and Eigenvalues / 8:
Polynomials and Matrices / 9:
Triangulation of Matrices and Linear Maps / 10:
Polynomials and Primary Decomposition / 11:
Convex Sets / 12:
Vector Spaces / 1:
Matrices / 2:
Linear Mappings / 3:
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