Definition:Norm/Unital Algebra

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


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