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Table of contents (4 chapters)
Keywords
About this book
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
Bibliographic Information
Book Title: Algebra II
Book Subtitle: Chapters 4 - 7
Authors: Nicolas Bourbaki
DOI: https://doi.org/10.1007/978-3-642-61698-3
Publisher: Springer Berlin, Heidelberg
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eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag GmbH Germany, part of Springer Nature 2003
Softcover ISBN: 978-3-540-00706-7Published: 16 April 2003
eBook ISBN: 978-3-642-61698-3Published: 01 December 2013
Edition Number: 1
Number of Pages: VII, 453
Additional Information: Original French edition published by Masson, Paris, 1981
Topics: Algebra