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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
Sommario
One Arithmetic Theory of Fields.- I. Valuated Fields.- II. Dedekind Theory of Ideals.- III. Fields of Number Theory.- Two Abstract Theory of Quadratic Forms.- IV. Quadratic Forms and the Orthogonal Group.- V. The Algebras of Quadratic Forms.- Three Arithmetic Theory of Quadratic Forms over Fields.- VI. The Equivalence of Quadratic Forms.- VII. Hilbert's Reciprocity Law.- Four Arithmetic Theory of Quadratic Forms over Rings.- VIII. Quadratic Forms over Dedekind Domains.- IX. Integral Theory of Quadratic Forms over Local Fields.- X. Integral Theory of Quadratic Forms over Global Fields.
Info autore
Timothy O'Meara was born on January 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 1996 he was provost of the University of Notre Dame.
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"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
