Algebra II
Produktnummer:
183f8d6ec0d7d34091b218a868a5aac26f
Autor: | Bourbaki, N. |
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Themengebiete: | MSC (2000): 12-02, 13-02, 12Fxx, 12J15, 13F10, 13C10, 12E05, YellowSale2006 algebra commutative fields ordered fields ordered groups polynomials power series principal ideal domains rational fractions |
Veröffentlichungsdatum: | 16.04.2003 |
EAN: | 9783540007067 |
Sprache: | Englisch |
Seitenzahl: | 453 |
Produktart: | Kartoniert / Broschiert |
Verlag: | Springer Berlin |
Untertitel: | Chapters 4 - 7 |
Produktinformationen "Algebra II"
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, regularextensions. 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 FractionsChapter V: Commutative FieldsChapter VI: Ordered Groups and FieldsChapter VII: Modules Over Principal Ideal Domains

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