Normed algebra explained

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

\forall x,y\in A \|xy\|\le\|x\|\|y\|.

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

See also

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

External reading

• Encyclopedia: Normed Algebra. Encyclopaedia of Mathematics. 20 May 2018.