Normed algebra

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

[math]\displaystyle{ \forall x,y\in A\qquad \|xy\|\le\|x\|\|y\|. }[/math]

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. https://www.encyclopediaofmath.org/index.php/Normed_algebra. Retrieved 20 May 2018.