Axiom:Ring Compatible Ordering Axioms

Definition
Let $\struct {R, +, \circ}$ be a ring whose zero is $0_R$.

Let $\preccurlyeq$ be an ordering $\preccurlyeq$ on $R$.

$\preccurlyeq$ is an ordering compatible with ring structure $\preccurlyeq$ satisfies the axioms:

These criteria are called the ring compatible ordering axioms.

Also see

 * Definition:Ordered Ring