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88,92 €In this monograph the authors extend the classical algebraic theory of quadratic forms over fields to diagonal quadratic forms with invertible entries over broad classes of commutative, unitary rings where -1 is not a sum of squares and 2 is invertible. They accomplish this by:
(1) Extending the classical notion of matrix isometry of forms to a suitable notion of T-isometry, where T is a preorder of the given ring, A, or T=A2.
(2) Introducing in this context three axioms expressing simple properties of (value) representation of elements of the ring by quadratic forms, well-known to hold in the field case.
Authors
M. Dickmann, Institut de Mathématiques de Jussieu-Paris Rive Gauche, France.
F. Miraglia, University of São Paulo, Brasil
Table of Contents
Basic concepts
Rings and special groups
The notion of T-faithfully quadratic ring. Some basic consequences
Idempotents, Products and T-isometry
First-order axioms for quadratic faithfulness
Rings with many units
Transversality of representation in p-rings with bounded inversion
Reduced f-rings
Strictly representable rings
Quadratic form theory over faithfully quadratic rings
Bibliography
Index of symbols
Subject index
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