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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 Texts in Mathematics

Graduate Studies in Mathematics

Mathematics Encyclopedia

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