End GringMx.
Definition gset_mx (A : {set gT}) := \sum_(x in A) aG x.
Local Notation tG := #|pred_of_set (classes (gval G))|.
Definition classg_base := \matrix_(k < tG) mxvec (gset_mx (enum_val k)).
Let groupCl : {in G, forall x, {subset x ^: G <= G}}.

Lemma regular_module_ideal m (M : 'M_(m, nG)) :
mxmodule aG M = right_mx_ideal R_G (M *m R_G).