Definition:Multiplicative Inverse

Definition
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:
 * $a \oplus b = 1 = b \oplus a$