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

Sources

There are no source works cited for this page. Source citations are highly desirable, and mandatory for all definition pages. Definition pages whose content is wholly or partly unsourced are in danger of having such content deleted. To discuss this page in more detail, feel free to use the talk page.