The stable property of projective dimension

Abstract

We introduce the concept of monomial ideals with stable projective dimension, as a generalization of the Cohen-Macaulay property. Indeed, we study the class of monomial ideals I, whose projective dimension is stable under monomial localizations at monomial prime ideals p, with height p ≥ pd S/I. We study the relations between this property and other sorts of Cohen-Macaulayness. Finally, we characterize some classes of polymatroidal ideals with stable projective dimension.2010 Mathematics Subject Classification. 13F20, 05E40.