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Quadratic Forms Over Semilocal Rings

R. Baeza, "Quadratic Forms Over Semilocal Rings"
1978 | pages: 205 | ISBN: 3540088458, 0387088458 | DJVU | 1,3 mb

The algebraic theory of quadratic forms originates from the well-known paper [W] of Witt A937), where he introduced for the first time the so called Witt ring of a field, i.e. the ring of all quadratic forms over a field with respect to a certain equivalence relation (compare ยง4, chap.I in this work). The study of this ring and related questions is essentially what we understand by the algebraic theory of quadratic forms. Thirty years after the appearance of Witt's work, Pfister succeeded in his important papers [Pf]- 0 -> in giving the first results on the structure of the Witt ring of a field of characteristic not 2. Since Pfister's work appeared twelve years ago, a lot researchs on this subject have been made. Lam succeeded in writing down many of these researchs in his fine book [L], which is perhaps today the best source to which a student of the algebraic theory of quadratic forms may turn for a comprehensive treatment of this subject. Besides of the theory over fields a corresponding theory of quadratic forms over more general domains has been growing up.
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