Definition:Normed Algebra

Definition
Let $R$ be a division ring with norm $\norm {\,\cdot\,}_R$.

A normed algebra over $R$ is a pair $\struct {A, \norm{\,\cdot\,} }$ where:
 * $A$ is a algebra over $R$
 * $ \norm{\,\cdot\,} $ is a norm on $A$.

Normed unital algebra
A normed unitary algebra over $R$ is a pair $\struct {A, \norm {\,\cdot\,} }$ where:
 * $A$ is a unital algebra over $R$
 * $\norm {\,\cdot\,}$ is a norm on $A$.

Also see

 * Definition:Normed Vector Space

Special cases

 * Definition:Banach Algebra