Faithfully quadratic rings
Author(s)
Bibliographic Information
Faithfully quadratic rings
（Memoirs of the American Mathematical Society, v. 238,
American Mathematical Society, 2015
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Note
Bibliography: p. 121-123
Includes index
Description and Table of Contents
Description
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 $T = A^2$. (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.
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
by "Nielsen BookData"