\begin{definition}[Definition:Positive Definite (Ring)]
Let $\struct {R, +, \times}$ be a ring whose zero is denoted $0_R$.
Let $f: R \to \R$ be a (real-valued) function on $R$.
Then $f$ is '''positive definite''' {{iff}}:
:$\forall x \in R: \begin {cases} \map f x = 0 & : x = 0_R \\ \map f x > 0 & : x \ne 0_R \end {cases}$
Category:Definitions/Ring Theory
\end{definition}