Category:Normed Division Algebras

From ProofWiki
Jump to navigation Jump to search

This category contains results about Normed Division Algebras.
Definitions specific to this category can be found in Definitions/Normed Division Algebras.

Let $\struct {A_F, \oplus}$ be a unitary algebra where $A_F$ is a vector space over a field $F$.

Then $\struct {A_F, \oplus}$ is a normed divison algebra if and only if $A_F$ is a normed vector space such that:

$\forall a, b \in A_F: \norm {a \oplus b} = \norm a \norm b$

where $\norm a$ denotes the norm of $a$.