  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.

Commutative Algebra