Definition:Norm/Ring

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:

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:Field Norm of Quaternion, which is actually not a norm, as shown in Field Norm of Quaternion is not Norm.


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