Editing Field extension (section)

== Extension of scalars ==
{{main|Extension of scalars}}
Given a field extension, one can "[[Extension of scalars|extend scalars]]" on associated algebraic objects. For example, given a real vector space, one can produce a complex vector space via [[complexification]]. In addition to vector spaces, one can perform extension of scalars for [[associative algebra]]s defined over the field, such as polynomials or [[group ring|group algebra]]s and the associated [[group representation]]s. Extension of scalars of polynomials is often used implicitly, by just considering the coefficients as being elements of a larger field, but may also be considered more formally. Extension of scalars has numerous applications, as discussed in [[extension of scalars#Applications|extension of scalars: applications]].