Definition:Normed Algebra

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Definition

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


A normed algebra over $R$ is a pair $\struct {A, \norm{\,\cdot\,} }$ where:

$A$ is a algebra over $R$
$ \norm{\,\cdot\,} $ is a norm on $A$.


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