Definition:Positive Definite (Ring)

Definition
Let $\left({R, +, \times}\right)$ be a division ring whose zero is denoted $0_R$.

Let $f: R \to \R_{\ge 0}$ be a mapping on $R$.

Then $f$ is positive definite :


 * $\forall x \in R: f \left({x}\right) = 0 \iff x = 0_R$