On ordered monoid rings over a quasi-Baer ring

A ring R is called (left principally) quasi-Baer if the left annihilator of every (principal) left ideal of R is generated by an idempotent. We show t hat if R is (left principally) quasi-Baer and G is an ordered monoid, then the monoid ring RG is again (left principally) quasi-Baer. When R is (left principally) quasi-Baer and G is an ordered group acting on R, we give a ne cessary and sufficient condition for the skew group ring R#G to be (left pr incipally) quasi-Baer.