Definition:Star-Algebra

Definition
Let $A = \left({A_F, \oplus}\right)$ be an unitary division algebra.

Let $A$ have a mapping $*: A \to A$ such that:
 * $\forall a \in A: \left({a^*}\right)^* = a$
 * $\forall a, b \in A: \left({a \oplus b}\right)^* = b^* \oplus a^*$

Then $A$ is a $*$-algebra (usually voiced star-algebra).

The mapping $*: A \to A$ is a conjugation on $A$.