Category:Definitions/Unitary Division Algebras

This category contains definitions related to Unitary Division Algebras.
Related results can be found in Category:Unitary Division Algebras.

Let $\struct {A_F, \oplus}$ be a division algebra.

Then $\struct {A_F, \oplus}$ is a unitary division algebra if and only if it has an identity element $1_{A_F}$ called a unit for $\oplus$, that is:

$\exists 1_{A_F} \in A_F: \forall a \in A_F: a \oplus 1_{A_F} = 1_{A_F} \oplus a = a$

The unit is usually denoted $1$ when there is no source of confusion with the identity elements of the underlying structures of the division algebra.