Algebra II

<P>This is a softcover reprint of the English translation of 1990 of the revised and expanded version of Bourbaki's <EM>Alg��bre</EM> Chapters 4 to 7 (1981). </P><P>This completes <EM>Algebra</EM> 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.</P><P>Chapter IV: Polynomials and Rational Fractions</P><P>Chapter V: Commutative Fields</P><P>Chapter VI: Ordered Groups and Fields</P><P>Chapter VII: Modules Over Principal Ideal Domains</P><P> </P>