Algebra II: Chapters 4 - 7

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Springer Science & Business Media, 1 дек. 2013 г. - Всего страниц: 453

This is a softcover reprint of the English translation of 1990 of the revised and expanded version of Bourbaki's, Algèbre, Chapters 4 to 7 (1981).

This completes Algebra, 1 to 3, by establishing the theories of commutative fields and modules over a principal ideal domain. Chapter 4 deals with polynomials, rational fractions and power series. A section on symmetric tensors and polynomial mappings between modules, and a final one on symmetric functions, have been added. Chapter 5 was entirely rewritten. After the basic theory of extensions (prime fields, algebraic, algebraically closed, radical extension), separable algebraic extensions are investigated, giving way to a section on Galois theory. Galois theory is in turn applied to finite fields and abelian extensions. The chapter then proceeds to the study of general non-algebraic extensions which cannot usually be found in textbooks: p-bases, transcendental extensions, separability criterions, regular extensions. Chapter 6 treats ordered groups and fields and based on it is Chapter 7: modules over a p.i.d. studies of torsion modules, free modules, finite type modules, with applications to abelian groups and endomorphisms of vector spaces. Sections on semi-simple endomorphisms and Jordan decomposition have been added.

Chapter IV: Polynomials and Rational Fractions

Chapter V: Commutative Fields

Chapter VI: Ordered Groups and Fields

Chapter VII: Modules Over Principal Ideal Domains

 

Избранные страницы

Содержание

Algebraically closed extensions V 19
v
MODULES OVER PRINCIPAL IDEAL DOMAINS VII 1
vii
Regular extensions
17
Galois descent V
62
Galois cohomology V
64
Artins theorem V
65
The fundamental theorem of Galois theory V
67
Change of base field V
69
Duality of ZnZmodules V
86
Kummer theory V
88
ArtinSchreier theory V
91
Finite fields V
93
Algebraic extensions of a finite field V
94
The Galois group of the algebraic closure of a finite field V
96
Cyclotomic polynomials over a finite field V
97
pradical extensions of height 1 V
98

The normal basis theorem V
72
Finite Isets and etale algebras V
75
The structure of quasiGalois extensions V
76
Abelian extensions V
77
Roots of unity V
78
Primitive roots of unity V
79
Cyclotomic extensions V
81
Irreducibility of cyclotomic polynomials V
83
Cyclic extensions V
85
Exercises on 2
2
Differentials and pbases V 100
3
Exercises on 8
8
Exercises on 14
14
Exercises on 15
15
Exercises on 17
17
algebras of derivations V 104
459
Авторские права

Другие издания - Просмотреть все

Algebra II: Chapters 4 - 7
N. Bourbaki
Ограниченный просмотр - 2003
Algebra II: Chapters 4 - 7
N. Bourbaki
Недоступно для просмотра - 1990
Algebra II: Chapters 4 - 7
N. Bourbaki
Недоступно для просмотра - 1990
Просмотреть все »

Часто встречающиеся слова и выражения

A-module a₁ abelian algebraic closure algebraic extension algebraically disjoint algebraically free automorphism bijective canonical coefficients commutative field commutative ring containing coprime COROLLARY cyclic Deduce defined denote direct sum endomorphism equation equivalent etale exists a unique extension of finite family of elements field of characteristic field of fractions finite degree follows formal power series formula Galois extension Galois group hence homomorphism implies indeterminates infinite injective integral domain invertible irreducible polynomial isomorphic K-algebra K-automorphism lattice ordered Lemma Let f linearly disjoint mapping matrix minimal polynomial module monic necessary and sufficient nilpotent non-zero ordered field ordered group p-radical extension polynomial ƒ polynomial in K[X prime number principal ideal domain Prop PROPOSITION prove rational fractions resp roots of unity separable algebraic Show subextension subfield subgroup submodule subring subset Suppose theorem transcendence basis vector space whence ΕΙ

Библиографические данные

НазваниеAlgebra II: Chapters 4 - 7
Elements of Mathematics
АвторN. Bourbaki
Перевод:P.M. Cohn, J. Howie
Издание:иллюстрированное, перепечатанное
ИздательSpringer Science & Business Media, 2013
ISBN3642616984, 9783642616983
Количество страницВсего страниц: 453
  
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