quality:correction, linguistic:paraphrasing, structural:expansion, stylistic:style_transfer
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 V F:= V ⊗ K F {\displaystyle V_{F}:=V\otimes _{K}F}. So if A is an algebra over K, then A F {\displaystyle A_{F}} is an algebra over F.