\begin{definition}[Definition:Multiplicative Inverse]
Let $\strut {A_F, \oplus}$ be a unitary algebra whose unit is $1$ and whose zero is $0$.
Let $a \in A_F$ such that $a \ne 0$.
A '''multiplicative inverse''' of $a$ is an element $b \in A_F$ such that:
:$a \oplus b = 1 = b \oplus a$
\end{definition}