A NOTE ON DEFINITE QUADRATIC SPACES AND BAER ORDERINGS

Original Articles

A NOTE ON DEFINITE QUADRATIC SPACES AND BAER ORDERINGS

Published in: Quaestiones Mathematicae
Volume 10 , issue 4 , 1987 , pages: 317–320
DOI: 10.1080/16073606.1987.9632131
Author(s): Robert Piziak Department of Mathematics, U.S.A.
Keywords: Primary 12J15 , 12J20 , 16A28 , 16A40 , Secondary 10C05 , 15A63
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Abstract

Let (k,E,Φ) be a definite quadratic space of dimension at least 3. Under certain assumptions, the set {Φ(z,z)|z ≠ in E} is a Baer ordering for k. Under somewhat more restrictive assumptions, the product of positive elements will be positive and a Cauchy-Schwartz Inequality will hold.
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