Normed algebra

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

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

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

See also

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

External reading

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