Local Notation aG := regular_repr.
Definition group_ring := enveloping_algebra_mx aG.
Local Notation R_G := group_ring.
Definition gring_row : 'M[R]_nG -> 'rV_nG := row (gring_index 1).
Canonical gring_row_linear := [linear of gring_row].

Lemma gring_row_mul A B : gring_row (A *m B) = gring_row A *m B.