- Main Menu-

Catalogue Tag Display

MARC 21

Algebra II: Chapters 4–7
Tag	Description
020	$a9783642616983
082	$a512
099	$aOnline resource: Springer
100	$aBourbaki, Nicolas.
245	$aAlgebra II$h[EBook]$bChapters 4–7$cby Nicolas Bourbaki.
260	$aBerlin, Heidelberg$bSpringer$c2003.
300	$aVII, 453 pages$bonline resource.
336	$atext
338	$aonline resource
440	$aElements of Mathematics
505	$aIV. — Polynomials and rational fractions -- V. — Commutative fields -- VI. — Ordered groups and fields -- VII. — Modules over principal ideal domains -- Index of notations -- Index of terminology.
520	$aThis 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 .
538	$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
710	$aSpringerLink (Online service)
830	$aElements of Mathematics
856	$uhttp://dx.doi.org/10.1007/978-3-642-61698-3