In [[abstract algebra]], a '''module''' is a generalization of a [[vector space]]. In a vector space the set of [[scalars]] forms a [[field_(mathematics)|field]], whereas in a module the scalars justneed formonly be a [[ring_(mathematics)|ring]]. Much of the theory of modules consists of recovering desirable properties of vector spaces in the realm of modules over certain rings. However, modules can be quite a bit more complicated than vector spaces; for instance, not all modules have a [[basis (linear algebra)|basis]].
