Andere Kunden interessierten sich auch für
![Algèbre / Eléments de Mathématique Chapitres.1-3]( "Algèbre / Eléments de Mathématique Chapitres.1-3")
Algèbre / Eléments de Mathématique Chapitres.1-348,99 €![Groupes et algèbres de Lie / Eléments de Mathématique]( "Groupes et algèbres de Lie / Eléments de Mathématique")
Groupes et algèbres de Lie / Eléments de Mathématique33,99 €![Algèbre commutative]( "Algèbre commutative")
Algèbre commutative37,99 €![Homological Algebra]( "Homological Algebra")
Homological Algebra83,99 €![Algebra IX]( "Algebra IX")
Algebra IX83,99 €![Algebra Interactive!]( "Algebra Interactive!")
Algebra Interactive!37,99 €![Algebra]( "Algebra")
Algebra52,99 €
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.
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.
From the reviews:
"Bourbaki's 'Algebra' focus on a systematic, rigorous and comprehensive treatment of field theory, Galois theory, and the theory of modules over a principal domain, together with numerous related topics and applications. ... Bourbaki's Chapters 4-7 of Book II will remain an everlasting treasure in the textbook literature of abstract algebra." (Werner Kleinert, Zentralblatt MATH, Vol. 1139 (17), 2008)
"Bourbaki's 'Algebra' focus on a systematic, rigorous and comprehensive treatment of field theory, Galois theory, and the theory of modules over a principal domain, together with numerous related topics and applications. ... Bourbaki's Chapters 4-7 of Book II will remain an everlasting treasure in the textbook literature of abstract algebra." (Werner Kleinert, Zentralblatt MATH, Vol. 1139 (17), 2008)