Algebra

著者

• Bourbaki, Nicolas

書誌事項

Algebra

Nicolas Bourbaki

（Elements of mathematics / Nicolas Bourbaki）

Springer-Verlag, c1989-

• 1, ch. 1-3 : gw
• 1, ch. 1-3 : gw : pbk
• 1, ch. 1-3 : us
• 2, ch. 4-7 : gw
• 2, ch. 4-7 : gw : pbk
• 2, ch. 4-7 : us

タイトル別名

Algèbre

注記

Translation of: Algèbre

Vol.2. translated by P.M. Cohn & J. Howie

Includes bibliographies and index

内容説明・目次

巻冊次

2, ch. 4-7 : gw : pbk ISBN 9783540007067

内容説明

This is a softcover reprint of chapters four through seven of the 1990 English translation of the revised and expanded version of Bourbaki's Algebre. Much material was added or revised for this edition, which thoroughly establishes the theories of commutative fields and modules over a principal ideal domain.

目次

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.

巻冊次

1, ch. 1-3 : gw ISBN 9783540193739

内容説明

This softcover reprint of the 1974 English translation of the first three chapters of Bourbaki's Algebre gives a thorough exposition of the fundamentals of general, linear, and multilinear algebra. The first chapter introduces the basic objects, such as groups and rings. The second chapter studies the properties of modules and linear maps, and the third chapter discusses algebras, especially tensor algebras.

目次

Algebraic Structures.- Linear Algebra.- Tensor Algebras, Exterior Algebras.- Symmetric Algebras.- Historical Notes.

巻冊次

2, ch. 4-7 : gw ISBN 9783540193753

内容説明

The English translation of the new and expanded version of Bourbaki's "Algbre", Chapters 4 to 7 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 has been 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.

巻冊次

1, ch. 1-3 : gw : pbk ISBN 9783540642435

内容説明

This softcover reprint of the 1974 English translation of the first three chapters of Bourbaki's Algebre gives a thorough exposition of the fundamentals of general, linear, and multilinear algebra. The first chapter introduces the basic objects, such as groups and rings. The second chapter studies the properties of modules and linear maps, and the third chapter discusses algebras, especially tensor algebras.

目次

Algebraic Structures.- Linear Algebra.- Tensor Algebras, Exterior Algebras.- Symmetric Algebras.- Historical Notes.

「Nielsen BookData」 より

詳細情報

• NII書誌ID(NCID): BA06628444
• ISBN:
  • 3540193731
  • 3540642439
  • 0387193731
  • 3540193758
  • 9783540007067
  • 0387193758
• LCCN: 88031211
• 出版国コード: gw
• タイトル言語コード: eng
• 本文言語コード: eng
• 原本言語コード: fre
• 出版地: Berlin ; Tokyo
• ページ数/冊数: v.
• 大きさ: 24 cm
• 分類:
  • LCC : QA155
  • DC19 : 512
  • NDC7 : 410
  • NDC7 : 411
• 件名:
  • LCSH : Algebra
• 親書誌ID:
  • BA01043035