The stable property of projective dimension

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 [Formula: see text], whose projective dimension is stable under monomial localizations at monomial prime ideals [Formula: see text], with [Formula: see text]. 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.

On Standard Invariants of Bi-polymatroidal Ideals

The standard invariants of the bi-polymatroidal ideals of Veronese type are computed.

Monomial Ideals with Primary Components given by Powers of Monomial Prime Ideals

We characterize monomial ideals which are intersections of powers of monomial prime ideals and study classes of ideals with this property, among them polymatroidal ideals.