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In mathematics, a '''normed algebra''' ''A'' refers to an [[algebra over a field]] which has a sub-multiplicative [[norm (mathematics)|norm]]:
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<center><math>\forall x,y\in A\qquad \|xy\|\le\|x\|\|y\|</math></center>
 
Optionally, it is sometimes required to have a [[Algebra_over_a_field#Unital_algebras|multiplicative identity]] 1{{sub|''A''}} such as ║1{{sub|''A''}}║ = 1.
 
==See also==
* [[Banach algebra]]
* [[Composition algebra]]
* [[Division algebra]]
* [[Gelfand–Mazur theorem]]
* [[Hurwitz's theorem (composition algebras)]]
 
==External Reading==
{{cite web|url=http://www.encyclopediaofmath.org/index.php/Normed_algebra|title=Normed Algebra|work=Encyclopaedia of Mathematics|accessdate=6 June 2013}}
 
 
 
 
{{algebra-stub}}
 
[[Category:Algebras]]

Latest revision as of 04:45, 24 December 2014

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