# .

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.

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