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# 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 1A such as ║1A║ = 1.

See also

Banach algebra

Composition algebra

Division algebra

Gelfand–Mazur theorem

Hurwitz's theorem (composition algebras)

External Reading

"Normed Algebra". Encyclopaedia of Mathematics. Retrieved 6 June 2013.

Undergraduate Texts in Mathematics

Graduate Studies in Mathematics

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