Algebra

著者

• Cohn, P. M. (Paul Moritz)

書誌事項

Algebra

P.M. Cohn

J. Wiley, c1982-c1991

2nd ed

• v. 1
• v. 1 : pbk
• v. 2
• v. 2 : pbk
• v. 3
• v. 3 : pbk

注記

Includes bibliographies and index

内容説明・目次

巻冊次

v. 2 ISBN 9780471922346

内容説明

The main emphasis of this revised algebra textbook is on fields, rings and modules. The text includes new chapters on the representative theory of finite groups, coding theory and algebraic language theory. Sets, lattices, categories and graphs are introduced at the beginning of the text. The text, which has been rewritten with the aim of making the subject easier to grasp, contains simplified proofs and many new illustrations and exercises.

目次

• Conventions on terminology - table of interdependence of chapters (Leitfaden) - sets, Zorn's lemma and well-ordered sets
• lattices - Boolean algebras, Mobius functions
• field theory - the fundamental theorem of Galois theory
• modules
• rings and algebras - the Wedderburn structure theorems
• quadratic forms and ordered fields - Witt's cancellation theorem and the Witt group of a field
• representation theory of finite groups - Maschke's theorem, the theorems of Burnside and Frobenius
• valuation theory
• commutative rings - Notherian rings, Dedekind domains, the Hilbert Nullstellensatz
• coding theory
• languages and automata.

巻冊次

v. 2 : pbk ISBN 9780471922353

内容説明

The main emphasis of this revised algebra textbook is on fields, rings and modules. The text includes new chapters on the representative theory of finite groups, coding theory and algebraic language theory. Sets, lattices, categories and graphs are introduced at the beginning of the text. The text, which has been rewritten with the aim of making the subject easier to grasp, contains simplified proofs and many new illustrations and exercises.

目次

• Conventions on terminology - table of interdependence of chapters (Leitfaden) - sets, Zorn's lemma and well-ordered sets
• lattices - Boolean algebras, Mobius functions
• field theory - the fundamental theorem of Galois theory
• modules
• rings and algebras - the Wedderburn structure theorems
• quadratic forms and ordered fields - Witt's cancellation theorem and the Witt group of a field
• representation theory of finite groups - Maschke's theorem, the theorems of Burnside and Frobenius
• valuation theory
• commutative rings - Notherian rings, Dedekind domains, the Hilbert Nullstellensatz
• coding theory
• languages and automata.

巻冊次

v. 3 ISBN 9780471928409

内容説明

The expanded second edition of this text on algebra features greater discussion of numerous topics. These include matters related to graded algebra, group theory, linear groups, symplectic and orthogonal groups, Morita equivalence and the Krull-Schmidt theorem.

目次

• Part 1 Universal algebra: algebras and homomorphisms
• congruences and the isomorphism theorems
• free algebrae and varieties
• abstract dependence relations
• the diamond lemma
• ultraproducts
• the natural numbers. Part 2 Multilinear algebra: graded algebras
• free algebras and tensor algebras
• the hilbert series of a graded algebra or module
• the exterior algebra on a module. Part 3 Homological algebra: additive and abelian categories
• functors on abelian categories
• homological dimension. Part 4 Further group theory: group extensions
• the Frattini subgroup and the pitting subgroup
• free groups
• linear groups. Part 5 Further field theory: algebraic dependence
• derivations
• infinite algebraic extensions
• Galois cohomology. Part 6 Algebras: the Frull-Schmidt theorem
• semiperfect rings
• the Morita context
• Fochschild cohomology and separable algebras. Part 7 Central simple algebras: the Brauer group
• charge of base field
• cyclic algebras. Part 8 Quadratic forms and ordered fields: the Clifford algebra of a quadratic space
• the Witt ring of a field
• the symplectic group
• the orthogonal group. Part 9 Koetherian rings and polynomial identities: rings of fractions
• skew polynomials and Laurent series
• Goldie's theorem
• PJ-algebras
• generic metrix rings and central polynemials
• generalized polynomial identities. Part 10 Rings without finitensee assumptions: the endemorphism ring of a vector space
• primitive rings
• semiprimitive rings and the Jacobeon radical
• algebras without a unit element. Part 11 Skew fields: the Dieudonne determinant
• pseudo-linear extensions.

巻冊次

v. 3 : pbk ISBN 9780471961093

内容説明

This is the third and final volume of a popular algebra textbook, which is being published in paperback at a reduced rate.

「Nielsen BookData」 より

詳細情報

• NII書誌ID(NCID): BA00890750
• ISBN:
  • 0471101680
  • 0471101699
  • 047192234X
  • 0471922358
  • 0471928402
  • 0471961094
• LCCN: 81021932
• 出版国コード: uk
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Chichester [Sussex] ; New York
• ページ数/冊数: 3 v.
• 大きさ: 23 cm
• 分類:
  • NDC8 : 411
  • LCC : QA154.2
  • DC19 : 512.9
• 件名:
  • LCSH : Algebra