Hilbert's Syzygy Theorem for monomial ideals

Year 2022, Volume: 32 Issue: 32, 80 - 85, 16.07.2022

Guillermo Alesandronı

https://doi.org/10.24330/ieja.1102307

Abstract

We give a new proof of Hilbert's Syzygy Theorem for monomial ideals. In addition, we prove the following. If $S=k[x_1,\dots ,x_n]$ 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 $\text{pd}\left(S/M\right)\le n-i$.

Keywords

Betti number, free resolution, monomial ideal

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