Local Notation "''R_' i" := (Wedderburn_subring i) : group_ring_scope.
Let sums_R : (\sum_i 'R_i :=: Socle sG *m R_G)%MS.

Lemma Wedderburn_mulmx0 i j A B :
i != j -> (A \in 'R_i)%MS -> (B \in 'R_j)%MS -> A *m B = 0.