Definition:Normed Unital Algebra

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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

• Results about normed unital algebras can be found here.

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