Quadratic and Hermitian Forms over Rings
Knus, Max-Albert
ISBN 10: 3642754031 ISBN 13: 9783642754036
Published by Springer, 2012
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This book presents the theory of quadratic and hermitian forms over rings in an algebraic setting. the main features are a detailed study of Clifford algebras, with applications to quadratic forms of low rank, and complete proofs of the stability, cancellation and splitting theorems in unitary K-theory. These theorems are applied to polynomial rings, to give quadratic analogues of the theorem of Quillen and Suslin on projective modules, and to Witt groups of regular rings. The book is addressed to advanced undergraduate and graduate students of algebra, as well as researchers in the field.
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Title: Quadratic and Hermitian Forms over Rings
Publisher: Springer
Publication Date: 2012
Binding: Soft cover
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Quadratic and Hermitian Forms over Rings
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. From its birth (in Babylon?) till 1936 the theory of quadratic forms dealt almost exclusively with forms over the real field, the complex field or the ring of integers. Only as late as 1937 were the foundations of a theory over an arbitrary field laid. This. Seller Inventory # 5069792
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Quadratic and Hermitian Forms over Rings (Grundlehren der mathematischen Wissenschaften)
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Quadratic and Hermitian Forms over Rings
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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - From its birth (in Babylon ) till 1936 the theory of quadratic forms dealt almost exclusively with forms over the real field, the complex field or the ring of integers. Only as late as 1937 were the foundations of a theory over an arbitrary field laid. This was in a famous paper by Ernst Witt. Still too early, apparently, because it took another 25 years for the ideas of Witt to be pursued, notably by Albrecht Pfister, and expanded into a full branch of algebra. Around 1960 the development of algebraic topology and algebraic K-theory led to the study of quadratic forms over commutative rings and hermitian forms over rings with involutions. Not surprisingly, in this more general setting, algebraic K-theory plays the role that linear algebra plays in the case of fields. This book exposes the theory of quadratic and hermitian forms over rings in a very general setting. It avoids, as far as possible, any restriction on the characteristic and takes full advantage of the functorial aspects of the theory. The advantage of doing so is not only aesthetical: on the one hand, some classical proofs gain in simplicity and transparency, the most notable examples being the results on low-dimensional spinor groups; on the other hand new results are obtained, which went unnoticed even for fields, as in the case of involutions on 16-dimensional central simple algebras. The first chapter gives an introduction to the basic definitions and properties of hermitian forms which are used throughout the book. Seller Inventory # 9783642754036
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Quadratic and Hermitian Forms over Rings
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ISBN 10: 3642754031
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Taschenbuch. Condition: Neu. Neuware -From its birth (in Babylon ) till 1936 the theory of quadratic forms dealt almost exclusively with forms over the real field, the complex field or the ring of integers. Only as late as 1937 were the foundations of a theory over an arbitrary field laid. This was in a famous paper by Ernst Witt. Still too early, apparently, because it took another 25 years for the ideas of Witt to be pursued, notably by Albrecht Pfister, and expanded into a full branch of algebra. Around 1960 the development of algebraic topology and algebraic K-theory led to the study of quadratic forms over commutative rings and hermitian forms over rings with involutions. Not surprisingly, in this more general setting, algebraic K-theory plays the role that linear algebra plays in the case of fields. This book exposes the theory of quadratic and hermitian forms over rings in a very general setting. It avoids, as far as possible, any restriction on the characteristic and takes full advantage of the functorial aspects of the theory. The advantage of doing so is not only aesthetical: on the one hand, some classical proofs gain in simplicity and transparency, the most notable examples being the results on low-dimensional spinor groups; on the other hand new results are obtained, which went unnoticed even for fields, as in the case of involutions on 16-dimensional central simple algebras. The first chapter gives an introduction to the basic definitions and properties of hermitian forms which are used throughout the book.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 544 pp. Englisch. Seller Inventory # 9783642754036
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Quadratic and Hermitian Forms over Rings
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Springer Berlin Heidelberg Jan 2012, 2012
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ISBN 13: 9783642754036
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -From its birth (in Babylon ) till 1936 the theory of quadratic forms dealt almost exclusively with forms over the real field, the complex field or the ring of integers. Only as late as 1937 were the foundations of a theory over an arbitrary field laid. This was in a famous paper by Ernst Witt. Still too early, apparently, because it took another 25 years for the ideas of Witt to be pursued, notably by Albrecht Pfister, and expanded into a full branch of algebra. Around 1960 the development of algebraic topology and algebraic K-theory led to the study of quadratic forms over commutative rings and hermitian forms over rings with involutions. Not surprisingly, in this more general setting, algebraic K-theory plays the role that linear algebra plays in the case of fields. This book exposes the theory of quadratic and hermitian forms over rings in a very general setting. It avoids, as far as possible, any restriction on the characteristic and takes full advantage of the functorial aspects of the theory. The advantage of doing so is not only aesthetical: on the one hand, some classical proofs gain in simplicity and transparency, the most notable examples being the results on low-dimensional spinor groups; on the other hand new results are obtained, which went unnoticed even for fields, as in the case of involutions on 16-dimensional central simple algebras. The first chapter gives an introduction to the basic definitions and properties of hermitian forms which are used throughout the book. 544 pp. Englisch. Seller Inventory # 9783642754036
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Quadratic and Hermitian Forms over Rings
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Paperback. Condition: New. Softcover reprint of the original 1st ed. 1991. Seller Inventory # LU-9783642754036
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Quadratic and Hermitian Forms over Rings
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ISBN 13: 9783642754036
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