Hilbert's Syzygy Theorem for monomial ideals

2017/11/27 by Alesandroni, Guillermo · 1 citation
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1711.09999

Abstract

We give a new proof of Hilbert's Syzygy Theorem for monomial ideals. In addition, we prove the following. If S=k[x₁,...,x_n] is a polynomial ring over a field, M is a squarefree monomial ideal in S, and each minimal generator of M has degree larger than i, then the projective dimension of S/M is at most n-i.

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