Definition:Normed Algebra

Definition
Let $R$ be a division ring with absolute value $|\cdot|$.

A normed algebra over $R$ is a pair $\left( A, \|\cdot\| \right)$ where:
 * $A$ is a algebra over $R$
 * $ \|\cdot\|$ is a norm on $A$.

Normed unital algebra
A normed unitary algebra over $R$ is a pair $\left( A, \|\cdot\| \right)$ where:
 * $A$ is a unital algebra over $R$
 * $ \|\cdot\|$ is a norm on $A$.

Also see

 * Definition:Normed Vector Space

Special cases

 * Definition:Banach Algebra