Abstract

In this talk we study how prime filtrations and squarefree Stanley decompositions of squarefree modules over the polynomial ring and over the exterior algebra behave with respect to Alexander duality. The results which we obtained suggest a lower bound for the regularity of a Z n-graded module in terms of its Stanley decompositions. For squarefree modules this conjectured bound is a direct consequence of Stanley's conjecture on Stanley decompositions. We show that for pretty clean monomial ideals and for monomial ideals with linear quotient our conjecture holds.



Information: