Answer to Question #23570 in Abstract Algebra for jeremy
statement turns out to be true for quotient algebras. To prove this, we may
assume that K = k. Consider the natural surjection ϕ : R → R'. Any simple left R'-moduleV may be viewed as a simple left R-module via ϕ. For any field extension L ⊇ k, V L remains simple as aleft RL-module. Therefore, V L is also asimple left R'L-module. This shows that V isabsolutely irreducible, so k is indeed a splitting field for R.
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