# Normed algebra

(Redirected from Normed division algebra)
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In mathematics, a normed algebra A refers to an algebra over a field which has a sub-multiplicative norm:

$\forall x,y\in A\qquad \|xy\|\le\|x\|\|y\|$

Optionally, it is sometimes required to have a multiplicative identity 1A such as ║1A║ = 1.

## External Reading

"Normed Algebra". Encyclopaedia of Mathematics. Retrieved 6 June 2013.