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