Faithfully Quadratic Rings

Download or Read eBook Faithfully Quadratic Rings PDF written by M. Dickmann and published by American Mathematical Soc.. This book was released on 2015-10-27 with total page 148 pages. Available in PDF, EPUB and Kindle.
Faithfully Quadratic Rings
Author :
Publisher : American Mathematical Soc.
Total Pages : 148
Release :
ISBN-10 : 9781470414689
ISBN-13 : 1470414686
Rating : 4/5 (89 Downloads)

Book Synopsis Faithfully Quadratic Rings by : M. Dickmann

Book excerpt: 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 is not a sum of squares and is invertible. They accomplish this by: (1) Extending the classical notion of matrix isometry of forms to a suitable notion of -isometry, where is a preorder of the given ring, , or . (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.


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