Canonical prodv_monoid := Monoid.Law prodvA prod1v prodv1.(* Centralisers and centers. *)

Definition centraliser1_vspace u := lker (amulr u - amull u).Fact algid_decidable U : decidable (exists e, is_algid e U).Definition has_algid : pred {vspace aT} := algid_decidable.

Lemma has_algidP {U} : reflect (exists e, is_algid e U) (has_algid U).