The weak Lefschetz property for m-full ideals and componentwise linear   ideals
  We give a necessary and sufficient condition for a standard graded Artinian ring defined by an m-full ideal, to have the weak Lefschetz property in terms of graded Betti numbers. This is a generalization of a theorem of Wiebe for componentwise linear ideals. We also prove that the class of componentwise linear ideals and that of completely m-full ideals coincide in characteristic zero and in positive characteristic, with the assumption that the generic initial ideal w.r.t. the graded reverse lexicographic order is stable. 
Tadahito Harima and Junzo Watanabe
math.AC