Editing Algebra over a field (section)

=== Extension of scalars ===
{{main|Extension of scalars}}
If we have a [[field extension]] ''F''/''K'', which is to say a bigger field ''F'' that contains ''K'', then there is a natural way to construct an algebra over ''F'' from any algebra over ''K''. It is the same construction one uses to make a vector space over a bigger field, namely the tensor product <math> V_F:=V \otimes_K F </math>. So if ''A'' is an algebra over ''K'', then <math>A_F</math> is an algebra over ''F''.