A NOTE ON DEFINITE QUADRATIC SPACES AND BAER ORDERINGS

摘要

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.