Algèbre
Chapitre 4 à 7
Seiten
2006
|
1. Réimpression inchangée de l'édition originale de 1981
Springer Berlin (Verlag)
978-3-540-34398-1 (ISBN)
Springer Berlin (Verlag)
978-3-540-34398-1 (ISBN)
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.
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.
Capter IV: Polinomials and Rational Fractions.- Chapter V: Commutative Fields.- Chapter VI: Ordered Groups and Fields.- Chapter VII: Modules Over Principal Ideal Domains.
Erscheint lt. Verlag | 6.12.2006 |
---|---|
Zusatzinfo | VIII, 422 p. |
Verlagsort | Berlin |
Sprache | französisch |
Maße | 156 x 234 mm |
Gewicht | 603 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
Naturwissenschaften ► Physik / Astronomie | |
Schlagworte | Algebra; Handbuch/Lehrbuch • commutative fields • Hardcover, Softcover / Mathematik/Arithmetik, Algebra • HC/Mathematik/Arithmetik, Algebra • MSC (2000): 12-02, 12E05, 12Fxx • MSC (2000): 12-02, 13-02, 12Fxx, 12J15, 13F10, 13C10, 12E05, • ordered fields • ordered groups • polynomials • power series • principal ideal domains • YellowSale2006 |
ISBN-10 | 3-540-34398-9 / 3540343989 |
ISBN-13 | 978-3-540-34398-1 / 9783540343981 |
Zustand | Neuware |
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