Definition:Norm/Unital Algebra

Definition
Let $R$ be a division ring with norm $\norm {\,\cdot\,}_R$. Let $A$ be an unital algebra over $R$ with unit $e$.

A norm on $A$ is an algebra norm $\norm{\,\cdot\,}: A \to \R_{\ge 0}$ such that:
 * $\norm e = 1$

Also see

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