Elements of Mathematics

Algebra II

Chapters 4 - 7

Authors: Bourbaki, N.

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About this Textbook

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

 

Table of contents (4 chapters)

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-3-642-61698-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $74.95
price for USA
  • ISBN 978-3-540-00706-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Algebra II
Book Subtitle
Chapters 4 - 7
Authors
Translated by
Howie, J., Cohn, P.M.
Series Title
Elements of Mathematics
Copyright
2003
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-61698-3
DOI
10.1007/978-3-642-61698-3
Softcover ISBN
978-3-540-00706-7
Edition Number
1
Number of Pages
VII, 453
Additional Information
Original French edition published by Masson, Paris, 1981
Topics