Introduction To Quadratic Forms by O. Timothy O'MearaIntroduction To Quadratic Forms by O. Timothy O'Meara

Introduction To Quadratic Forms

byO. Timothy O'Meara, O. T. O'meara

Paperback | December 14, 1999

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From the reviews: "O'Meara treats his subject from this point of view (of the interaction with algebraic groups). He does not attempt an encyclopedic coverage ...nor does he strive to take the reader to the frontiers of knowledge... . Instead he has given a clear account from first principles and his book is a useful introduction to the modern viewpoint and literature. In fact it presupposes only undergraduate algebra (up to Galois theory inclusive)... The book is lucidly written and can be warmly recommended.
J.W.S. Cassels, The Mathematical Gazette, 1965
"Anyone who has heard O'Meara lecture will recognize in every page of this book the crispness and lucidity of the author's style;... The organization and selection of material is superb... deserves high praise as an excellent example of that too-rare type of mathematical exposition combining conciseness with clarity...
R. Jacobowitz, Bulletin of the AMS, 1965
Biography of  O. Timothy O'MearaTimothy O'Meara was born on January 29, 1928. He was educated at the University of Cape Town and completed his doctoral work under Emil Artin at Princeton University in 1953. He has served on the faculties of the University of Otago, Princeton University and the University of Notre Dame. From 1978 to 199...
Title:Introduction To Quadratic FormsFormat:PaperbackDimensions:344 pagesPublished:December 14, 1999Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3540665641

ISBN - 13:9783540665649


Table of Contents

Prerequisites ad Notation Part One: Arithmetic Theory of Fields I Valuated Fields Valuations Archimedean Valuations Non-Archimedean valuations Prolongation of a complete valuation to a finite extension Prolongation of any valuation to a finite separable extension Discrete valuations II Dedekind Theory of Ideals Dedekind axioms for S Ideal theory Extension fields III Fields of Number Theory Rational global fields Local fields Global fields Part Two: Abstract Theory of Quadratic Forms VI Quadratic Forms and the Orthogonal Group Forms, matrices and spaces Quadratic spaces Special subgroups of On(V) V The Algebras of Quadratic Forms Tensor products Wedderburn's theorem on central simple algebras Extending the field of scalars The clifford algebra The spinor norm Special subgroups of On(V) Quaternion algebras The Hasse algebra VI The Equivalence of Quadratic Forms Complete archimedean fields Finite fields Local fields Global notation Squares and norms in global fields Quadratic forms over global fields VII Hilbert's Reciprocity Law Proof of the reciprocity law Existence of forms with prescribed local behavior The quadratic reciprocity law Part Four: Arithmetic Theory of Quadratic Forms over Rings VIII Quadratic Forms over Dedekind Domains Abstract lattices Lattices in quadratic spaces IX Integral Theory of Quadratic Forms over Local Fields Generalities Classification of lattices over non-dyadic fields Classification of Lattices over dyadic fields Effective determination of the invariants Special subgroups of On(V) X Integral Theory of Quadratic Forms over Global Fields Elementary properties of the orthogonal group over arithmetic fields The genus and the spinor genus Finiteness of class number The class and the spinor genus in the indefinite case The indecomposable splitting of a definite lattice Definite unimodular lattices over the rational integers Bibliography Index Bibliography Index

Editorial Reviews

"The exposition follows the tradition of the lectures of Emil Artin who enjoyed developing a subject from first principles and devoted much research to finding the simplest proofs at every stage." - American Mathematical Monthly