Algebra II - Chapters 4 - 7 (Paperback, 1st ed. 1990. 2nd printing 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, 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  

General

Imprint:	Springer-Verlag
Country of origin:	Germany
Release date:	April 2003
First published:	2003
Authors:	N. Bourbaki
Translators:	P. M. Cohn • J. Howie
Dimensions:	235 x 155 x 28mm (L x W x T)
Format:	Paperback
Pages:	453
Edition:	1st ed. 1990. 2nd printing 2003
ISBN-13:	978-3-540-00706-7
Languages:	English
Subtitles:	French
Categories:	Books > Science & Mathematics > Mathematics > Algebra > General Promotions
LSN:	3-540-00706-7
Barcode:	9783540007067

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