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Introduction to quadratic forms

Introduction to quadratic forms

Material type
단행본
Personal Author
O'Meara, O. T. (Onorato Timothy) , 1928-.
Title Statement
Introduction to quadratic forms / O. Timothy O'Meara.
Publication, Distribution, etc
Berlin ;   New York :   Springer ,   c2000.  
Physical Medium
xii, 342 p. : ill. ; 24 cm.
Series Statement
Classics in mathematics , 1431-0821
ISBN
3540665641 (pbk. : acid-free paper) 9783540665649
General Note
Originally published: 3rd corr. print. Berlin ; New York : Springer-Verlag, 1973, in series: Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berucksichtigung der Anwendungsgebiete ; Bd. 117.  
Bibliography, Etc. Note
Includes bibliographical references (p. [336]) and index.
Subject Added Entry-Topical Term
Forms, Quadratic.
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010 ▼a 99058347
020 ▼a 3540665641 (pbk. : acid-free paper)
020 ▼a 9783540665649
035 ▼a (KERIS)REF000005330936
040 ▼a DLC ▼c DLC ▼d DLC ▼d 211009
050 0 0 ▼a QA243 ▼b .O4 2000
082 0 0 ▼a 512/.74 ▼2 22
090 ▼a 512.74 ▼b O55i
100 1 ▼a O'Meara, O. T. ▼q (Onorato Timothy) , ▼d 1928-.
245 1 0 ▼a Introduction to quadratic forms / ▼c O. Timothy O'Meara.
260 ▼a Berlin ; ▼a New York : ▼b Springer , ▼c c2000.
300 ▼a xii, 342 p. : ▼b ill. ; ▼c 24 cm.
440 0 ▼a Classics in mathematics , ▼x 1431-0821
500 ▼a Originally published: 3rd corr. print. Berlin ; New York : Springer-Verlag, 1973, in series: Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berucksichtigung der Anwendungsgebiete ; Bd. 117.
504 ▼a Includes bibliographical references (p. [336]) and index.
650 0 ▼a Forms, Quadratic.
945 ▼a KINS

Holdings Information

No. Location Call Number Accession No. Availability Due Date Make a Reservation Service
No. 1 Location Science & Engineering Library/Sci-Info(Stacks2)/ Call Number 512.74 O55i Accession No. 121178670 Availability Available Due Date Make a Reservation Service B M

Contents information

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


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