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arXiv · 1810.00171

On the stable property of projective dimension

Somayeh Bandari·Raheleh Jafari
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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.

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Somayeh Bandari, Raheleh Jafari. 2018-09-29. On the stable property of projective dimension. https://arxiv.org/abs/1810.00171

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