  In this article first we prove that a special case of the order ideal
conjecture, originating from the work of Evans and Griffith in
equicharacteristic, implies the monomial conjecture due to M. Hochster. We
derive a necessary and sufficient condition for the validity of this special
case in terms certain syzygis of canonical modules of normal domains possessing
free summands. We also prove some special cases of this observation.
