Definition:Norm/Ring/Multiplicative

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

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

satisfying the (ring) multiplicative norm axioms:

Also see

 * Definition:Norm on Division Ring
 * Definition:Submultiplicative Norm on Ring
 * Definition:Norm on Vector Space
 * Definition:Topological Ring