Algebra : Chapters 4-7 Pt. 2 Paperback / softback
by Nicolas Bourbaki
Part of the Elements of Mathematics series
Paperback / softback
Description
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 FractionsChapter V: Commutative FieldsChapter VI: Ordered Groups and FieldsChapter VII: Modules Over Principal Ideal Domains
Information
-
Item not Available
- Format:Paperback / softback
- Pages:453 pages, biography
- Publisher:Springer-Verlag Berlin and Heidelberg GmbH & Co. K
- Publication Date:16/04/2003
- Category:
- ISBN:9783540007067
Information
-
Item not Available
- Format:Paperback / softback
- Pages:453 pages, biography
- Publisher:Springer-Verlag Berlin and Heidelberg GmbH & Co. K
- Publication Date:16/04/2003
- Category:
- ISBN:9783540007067
