\begin{definition}[Definition:Norm/Unital Algebra]
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:
:$\norm e = 1$
\end{definition}