Answer to Question #23568 in Abstract Algebra for jeremy
Show that for any finite-dimensional k-algebra R and any field extension K ⊇ k, (rad R)K ⊆ rad(RK).
It suffices to show that (rad R)Kannihilates any simple left RK-module V . But, Vis a composition factor of MK for some simple left R-moduleM. Since (rad R)M = 0, it follows that (rad R)KMK= 0. But then (rad R)KV = 0, as desired.
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