On the stable property of projective dimension

2018/09/29 by Bandari, Somayeh, Jafari, Raheleh
#05E40 #13F20 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1810.00171

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≥ \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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