Definition:Normed Unital Algebra

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

A normed unital 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:Unital Algebra over Ring
 * Definition:Norm on Unital Algebra
 * Definition:Normed Algebra
 * Definition:Normed Vector Space