  We define the strong Lefschetz property for finite graded modules over graded
Artinian algebras whose grading is not necessarily standard. We show that most
results which have been obtained for Artinian algebras with standard grading
can be extended for non-standard grading. Our results on the strong Lefschetz
property for non-standard grading can be used to prove that certain Artinian
complete intersections with standard grading have the strong Lefschetz
property.
