Algebra II: Chapters 4 - 7

di N. Bourbaki (Autore)

P.M. Cohn (Traduttore)

J. Howie (Traduttore)

Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, 2003

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  

• Autore: N. Bourbaki
• Traduttore: P.M. Cohn, J. Howie
• Editore: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
• Anno: 2003
• Rilegatura: Paperback / softback
• Pagine: 453 p.
• Dimensioni: 235 x 155 mm
• EAN: 9783540007067

Testo in English