Definition:Norm/Ring

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

A norm on $R$ is a submultiplicative norm on $R$.

That is, a mapping from $R$ to the non-negative reals:

Also see

 * Definition:Absolute Value, a well known norm as shown in Absolute Value is Norm.
 * Definition:Complex Modulus, a well known norm as shown in Complex Modulus is Norm.
 * Definition:Norm of Quaternion, a well known norm as shown in Quaternion Norm is Norm.


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