Definition:Division Algebra

Definition
Let $\struct {A_F, \oplus}$ be an algebra over field $F$ such that $A_F$ does not consist solely of the zero vector $\mathbf 0_A$ of $A_F$.

Also see

 * Equivalence of Definitions of Division Algebra


 * Division Algebra has No Zero Divisors, in which the two definitions are shown to be equivalent.