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

${\displaystyle \forall x,y\in A\qquad \|xy\|\leq \|x\|\|y\|.}$

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

See also

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

External reading

• "Normed Algebra". Encyclopaedia of Mathematics. Retrieved 20 May 2018.

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