We deal with the weak Lefschetz property (WLP) for Artinian standard graded Gorenstein algebras of codimension $3.$ We prove that many Gorenstein sequences force the WLP for such algebras. Moreover for every Gorenstein sequence $H$ of codimension $3$ we found several Gorenstein Betti sequences compatible with $H$ which again force the WLP. Finally we show that for every Gorenstein Betti sequence the general Artinian standard graded Gorenstein algebra with such Betti sequence has the WLP.
|Titolo:||On the Weak-Lefschetz property for Artinian Gorenstein algebras|
|Data di pubblicazione:||2013|
|Appare nelle tipologie:||1.1 Articolo in rivista|