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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
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
| Erscheinungsjahr: | 2003 |
|---|---|
| Fachbereich: | Arithmetik & Algebra |
| Genre: | Mathematik, Medizin, Naturwissenschaften, Technik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Reihe: | Elements of Mathematics |
| Inhalt: |
vii
453 S. |
| ISBN-13: | 9783540007067 |
| ISBN-10: | 3540007067 |
| Sprache: | Englisch |
| Herstellernummer: | 10670344 |
| Ausstattung / Beilage: | Paperback |
| Einband: | Kartoniert / Broschiert |
| Autor: | Bourbaki, N. |
| Übersetzung: |
Howie, J.
Cohn, P. M. |
| Auflage: | 1st ed. 1990. 2nd printing 2003 |
| Hersteller: |
Springer Berlin
Springer Berlin Heidelberg Elements of Mathematics |
| Verantwortliche Person für die EU: | Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com |
| Maße: | 235 x 155 x 25 mm |
| Von/Mit: | N. Bourbaki |
| Erscheinungsdatum: | 16.04.2003 |
| Gewicht: | 0,698 kg |
| Erscheinungsjahr: | 2003 |
|---|---|
| Fachbereich: | Arithmetik & Algebra |
| Genre: | Mathematik, Medizin, Naturwissenschaften, Technik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Reihe: | Elements of Mathematics |
| Inhalt: |
vii
453 S. |
| ISBN-13: | 9783540007067 |
| ISBN-10: | 3540007067 |
| Sprache: | Englisch |
| Herstellernummer: | 10670344 |
| Ausstattung / Beilage: | Paperback |
| Einband: | Kartoniert / Broschiert |
| Autor: | Bourbaki, N. |
| Übersetzung: |
Howie, J.
Cohn, P. M. |
| Auflage: | 1st ed. 1990. 2nd printing 2003 |
| Hersteller: |
Springer Berlin
Springer Berlin Heidelberg Elements of Mathematics |
| Verantwortliche Person für die EU: | Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com |
| Maße: | 235 x 155 x 25 mm |
| Von/Mit: | N. Bourbaki |
| Erscheinungsdatum: | 16.04.2003 |
| Gewicht: | 0,698 kg |
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