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On the stable property of projective dimension (1810.00171v1)
Published 29 Sep 2018 in math.AC and math.CO
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 $\fp$, with $\height \fp\geq \pd S/I$. 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.