Axiom:Submultiplicative Norm Axioms

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

Let $\norm {\, \cdot \,}: R \to \R_{\ge 0}$ be a submultiplicative norm on $R$.

The submultiplicative norm axioms are the conditions on $\norm {\, \cdot \,}$ which are satisfied for all elements of $R$ in order for $\norm {\, \cdot \,}$ to b a submultiplicative norm:

Also see

 * Axiom:Multiplicative Norm Axioms
 * Axiom:Norm Axioms (Vector Space)