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1.

図書

図書
Ehud de Shalit
出版情報: Boston ; Tokyo : Academic Press, c1987  ix, 154 p. ; 24 cm
シリーズ名: Perspectives in mathematics ; v. 3
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2.

図書

図書
edited by S. Iyanaga ; translated by K. Iyanaga
出版情報: Amsterdam : North-Holland Pub. Co. , New York : American Elsevier Pub. Co., 1975  xi, 541 p. ; 23 cm
シリーズ名: North-Holland mathematical library ; v. 8
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3.

図書

図書
Ludwig Holzer
出版情報: Leipzig : Teubner, 1966  186 p ; 24 cm
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4.

図書

図書
Jean-Pierre Serre
出版情報: Paris : Hermann, c1959  202 p. ; 24 cm
シリーズ名: Publications de l'Institut de mathématique de l'Université de Nancago ; 7
Actualités scientifiques et industrielles ; 1264
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5.

図書

図書
Jean-Pierre Serre
出版情報: New York ; Tokyo : Springer-Verlag, c1988  ix, 207 p. ; 25 cm
シリーズ名: Graduate texts in mathematics ; 117
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目次情報: 続きを見る
Summary of the Main Results
Algebraic Curves
Maps From a Curve to a Commutative Group
Singular Algebraic Curves
Generalized Jacobians
Class Field Theory
Group Extension and Cohomology
Bibliography
Supplementary Bibliography
Index
Summary of the Main Results
Algebraic Curves
Maps From a Curve to a Commutative Group
6.

図書

図書
Serge Lang
出版情報: Berlin ; New York : Springer, c1996  vi, 226 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1625
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7.

図書

図書
André Weil
出版情報: New York ; Berlin : Springer-Verlag, 1974  xviii, 325 p. ; 23 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; Bd. 144
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目次情報: 続きを見る
Affine Varieties
Projective Varieties
Structure of Correspondences
Chow's Theorem
Degree of a Projective Variety
Linear Systems
Curves and Their Genus
The Birational Geometry of Surfaces
Affine Varieties
Projective Varieties
Structure of Correspondences
8.

図書

図書
E. Artin and J. Tate
出版情報: [S.l.] : [s.n.], [19--?]  xvii, 259 p. ; 29 cm
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9.

図書

図書
P.E. Conner, J. Hurrelbrink
出版情報: Singapore : World Scientific, c1988  xi, 234 p. ; 23 cm
シリーズ名: Series in pure mathematics ; v. 8
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10.

図書

図書
Gregory Karpilovsky
出版情報: New York : M. Dekker, c1988  viii, 551 p. ; 26 cm
シリーズ名: Monographs and textbooks in pure and applied mathematics ; 120
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目次情報: 続きを見る
Preface
Preliminaries / Chapter 1.:
Notation and terminology / 1.:
Polynomial algebras / 2.:
Integral extensions / 3.:
Tensor products / 4.:
Module-theoretic prerequisites / 5.:
Topological prerequisites / 6.:
Classical Topics in Field Theory / Chapter 2.:
Algebraic extensions
Normal extensions
Separable, purely inseparable and simple extensions
Galois extensions
Finite fields, roots of unity and cyclotomic extensions
Norms, traces and their applications
Discriminants and integral bases / 7.:
Units in quadratic fields / 8.:
Units in pure cubic fields / 9.:
Finite Galois theory / 10.:
Profinite groups / 11.:
Infinite Galois theory / 12.:
Witt vectors / 13.:
Cyclic extensions / 14.:
Kummer theory / 15.:
Radical extensions and related results / 16.:
Degrees of sums in a separable field extension / 17.:
Galois cohomology / 18.:
The Brauer group of a field / 19.:
An interpretation of H[superscript 3 subscript O](G,E*) / 20.:
A cogalois theory for radical extensions / 21.:
Abelian p-extensions over fields of characteristic p / 22.:
Formally real fields / 23.:
Transcendental extensions / 24.:
Valuation Theory / Chapter 3.:
Valuations
Valuation rings and places
Dedekind domains
Completion of a field
Extensions of valuations
Valuations of algebraic number fields
Ramification index and residue degree
Structure of complete discrete valued fields
The equal characteristic case / A.:
The unequal characteristic case / C.:
The inertia field / D.:
Cyclotomic extensions of p-adic fields / E.:
Multiplicative Groups of Fields / Chapter 4.:
Some general observations
Infinite abelian groups
The Dirichlet-Chevalley-Hasse Unit Theorem
The torsion subgroup
Global fields
Algebraically closed, real closed and the rational p-adic fields
Local fields
Preparatory results
Extensions of algebraic number fields
Brandis's theorem
Fields with free multiplicative groups modulo torsion
A nonsplitting example
Embedding groups
Multiplicative groups under field extensions
Notes
Bibliography
Notation
Index
Preface
Preliminaries / Chapter 1.:
Notation and terminology / 1.:
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