Homological dimension and representation type of algebras under base field extension

We prove that for finite-dimensional associative algebras the finitistic global dimension in the sense of H. Bass and also the self-injective dimension are preserved under arbitrary extensions of the base field. Further, the global dimension, and as a consequence also finite representation type, are preserved under base field extensions which are separable in the sense of S. MacLane. The results are derived with the aid of ultraproduct-techniques and are applied to the model theory of finite dimensional algebras.