\begin{definition}[Definition:Normed Unital Algebra]
Let $R$ be a division ring with norm $\norm {\,\cdot\,}_R$.
A '''normed unital algebra''' over $R$ is a pair $\struct {A, \norm {\,\cdot\,} }$ where:
:$A$ is a unital algebra over $R$
:$\norm {\,\cdot\,}$ is a norm on $A$.
\end{definition}