Answer to Question #23569 in Abstract Algebra for jeremy

Question

Let R be a finite-dimensional k-algebra and let L ⊇ K ⊇ k be fields. Assume that L is a splitting field for R. Show that K is a splitting field for R iff, for every simple left RL-module M, there exists a (simple) left RK-module U such that UL ∼ M.