Introduction to Quadratic Forms Over Fields: 67 (Graduate Studies in Mathematics) - Softcover

Lam, T.Y.

Softcover

ISBN 10: 1470480174 ISBN 13: 9781470480172

Publisher: American Mathematical Society, 2005

Synopsis

A new version of the author's prize-winning Algebraic Theory of Quadratic Forms (Benjamin, 1973), this book gives a modern and self-contained introduction to the theory of quadratic forms over fields of characteristic not two. Starting with few prerequisites besides linear algebra, the author charts an expert course from Witt's classical theory of quadratic forms, quaternion and Clifford algebras, Artin-Schreier theory of formally real fields, and structural theorems on Witt rings, to the theory of Pfister forms, function fields, and field invariants. These main developments are seamlessly interwoven with excursions into Brauer-Wall groups, local and global fields, trace forms, Galois theory, and elementary algebraic K-theory, to create a uniquely original treatment of quadratic form theory over fields. Two new chapters totaling more than 100 pages have been added to the earlier incarnation of this book to take into account some of the newer results and more recent viewpoints in the area. As is characteristic of this author's expository style, the presentation of the main material in this book is interspersed with a copious number of carefully chosen examples to illustrate the general theory. This feature, together with a rich stock of some 280 exercises for the thirteen chapters, greatly enhances the pedagogical value of this book, both as a graduate text and as a reference work for researchers in algebra, number theory, field theory, algebraic geometry, algebraic topology, and geometric topology.

About this title

About the Author

T.Y. Lam, University of California, Berkeley, CA

Edition details

• Publisher: American Mathematical Society
• Publication date: 2005
• Language: English
• ISBN 10: 1470480174
• ISBN 13: 9781470480172
• Binding: Paperback
• Number of pages: 550