Algebra II
Springer Berlin (Verlag)
978-3-540-00706-7 (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, 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 Fractions
Chapter V: Commutative Fields
Chapter VI: Ordered Groups and Fields
Chapter VII: Modules Over Principal Ideal Domains
IV. - Polynomials and rational fractions.- V. - Commutative fields.- VI. - Ordered groups and fields.- VII. - Modules over principal ideal domains.- Index of notations.- Index of terminology.
| Erscheint lt. Verlag | 16.4.2003 |
|---|---|
| Übersetzer | P.M. Cohn, J. Howie |
| Zusatzinfo | VII, 453 p. |
| Verlagsort | Berlin |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 692 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Naturwissenschaften ► Physik / Astronomie | |
| Schlagworte | Algebra • commutative fields • finite field • Galois Theory • Mathematik; Handbuch/Lehrbuch • MSC (2000): 12-02, 13-02, 12Fxx, 12J15, 13F10, 13C • MSC (2000): 12-02, 13-02, 12Fxx, 12J15, 13F10, 13C10, 12E05, • ordered fields • ordered groups • polynomial • polynomials • power series • principal ideal domains • rational fractions • Torsion • YellowSale2006 |
| ISBN-10 | 3-540-00706-7 / 3540007067 |
| ISBN-13 | 978-3-540-00706-7 / 9783540007067 |
| Zustand | Neuware |
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