\begin{definition}[Definition:Normed Division Algebra]
Let $\left({A_F, \oplus}\right)$ be a unitary algebra where $A_F$ is a vector space over a field $F$.
Then $\left({A_F, \oplus}\right)$ is a normed divison algebra iff $A_F$ is a normed vector space such that:
:$\forall a, b \in A_F: \left \Vert{a \oplus b}\right \Vert = \left \Vert{a}\right \Vert \left \Vert{b}\right \Vert$
where $\left \Vert{a}\right \Vert$ denotes the norm of $a$.
\end{definition}