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We give a necessary and sufficient condition for a standard graded Artinianring defined by an m-full ideal, to have the weak Lefschetz property in termsof graded Betti numbers. This is a generalization of a theorem of Wiebe forcomponentwise linear ideals. We also prove that the class of componentwiselinear ideals and that of completely m-full ideals coincide in characteristiczero and in positive characteristic, with the assumption that the genericinitial ideal w.r.t. the graded reverse lexicographic order is stable.

The weak Lefschetz property for m-full ideals and componentwise linear ideals