An _algebra_ or an _algebra over a field_ is a [vector space](Vector%20spaces.md) over a field. The requirement that must be met for a vector space to be an algebra is that it must contain a multiplication that is _distributive_. ^198aff # Types of algebras We categorize algebras as _[associative](Associative%20algebras.md)_ or _[non-associative](Non-associative%20algebras.md)_. #MathematicalFoundations/Algebra/AbstractAlgebra/Algebras