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 of the form K[x(1), ... , x(n)]/I, where I is 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 Gin(I) w.r.t. the graded reverse lexicographic order is stable.