Faithfully Quadratic Rings

Ebook Details

Authors

M. Dickmann, F. Miraglia

Year 2015
Pages 129
Publisher Amer Mathematical Society
Language en
ISBN 9781470414689
File Size 1.05 MB
File Format PDF
Download Counter 99
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Ebook 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.