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＜電子ブック＞
Algebra II : Chapters 4 - 7 / by N. Bourbaki

版	1st ed. 2003.
出版者	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
出版年	2003
本文言語	英語
大きさ	VII, 453 p : online resource
冊子体	Algebra / Nicolas Bourbaki ; 1, ch. 1-3 : gw - 2, ch. 4-7 : us
著者標目	*Bourbaki, N author SpringerLink (Online service)
件　名	LCSH:Algebra FREE:Algebra
一般注記	IV. — Polynomials and rational fractions -- V. — Commutative fields -- VI. — Ordered groups and fields -- VII. — Modules over principal ideal domains -- Index of notations -- Index of terminology 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 Fractions Chapter V: Commutative Fields Chapter VI: Ordered Groups and Fields Chapter VII: Modules Over Principal Ideal Domains Accessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format Inaccessible, or known limited accessibility No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/978-3-642-61698-3

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