Definition:Norm/Ring/Submultiplicative

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

A submultiplicative norm on $R$ is a mapping from $R$ to the non-negative reals:
 * $\norm {\,\cdot\,}: R \to \R_{\ge 0}$

satisfying the (ring) submultiplicative norm axioms:

Also see

 * Definition:Norm on Ring
 * Definition:Multiplicative Norm on Ring
 * Definition:Norm on Ring
 * Definition:Norm on Vector Space