ENGLISH

Algebra II: Chapters 4-7

By N. Bourbaki

Book information

Publisher
Springer
Year
1990
ISBN
3540007067, 9783540007067
Language
english
Format
PDF
Filesize
7 MB (7418389 bytes)
Series
Elements of Mathematics
Edition
1
Pages
451\460
Topic
Mathematics Algebra
DPI
600
Orientation
portrait
Scanned
yes
Time added
2014-02-25 23:12:53

Description

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.

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