A special case of an operator ring: An algebra (occasionally, a linear or vector algebra) over a field, over a skew-field or over a commutative ring. Associative algebras (formerly described as "hypercomplex systems" ) and non-associative algebras are algebras in this sense.
Algebra. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Algebra&oldid=34322