Generic Initial Ideals, Graded Betti Numbers, and<i>k</i>-Lefschetz Properties
Generic Initial Ideals, Graded Betti Numbers, and<i>k</i>-Lefschetz Properties
Abstract We introduce the k-strong Lefschetz property and the k-weak Lefschetz property for graded Artinian K-algebras, which are generalizations of the Lefschetz properties. The main results are: 1. Let I be an ideal of R = K[x 1, x 2,…, x n ] whose quotient ring R/I has the n-SLP. …