Definition:Norm/Unital Algebra

This page is about Norm on Unital Algebra over Division Ring. For other uses, see Norm.

Definition

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

Let $A$ be an unital algebra over $R$ with unit $e$.

A norm on $A$ is an algebra norm $\norm{\,\cdot\,}: A \to \R_{\ge 0}$ such that:

$\norm e = 1$

Also see

• Definition:Norm on Division Ring
• Definition:Norm on Vector Space
• Definition:Norm on Algebra