Normed algebra

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 1_A such as ║1_A║ = 1.

See also

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