Normed algebra

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In mathematics, a normed algebra A is an algebra over a field which has a sub-multiplicative norm:

∀x,y∈A‖xy‖≤‖x‖‖y‖.

Some authors require it to have a multiplicative identity 1A such that ║1A║ = 1.

## See also

* Banach algebra
* Composition algebra
* Division algebra
* Gelfand–Mazur theorem
* Hurwitz's theorem (composition algebras)

## External reading

* "Normed Algebra". Encyclopaedia of Mathematics. https://www.encyclopediaofmath.org/index.php/Normed_algebra. Retrieved 20 May 2018.

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