Hilbert`s Syzygy Theorem for monomial ideals

Authors : Guillermo ALESANDRONI

Pages : 80-85

Doi:10.24330/ieja.1102307

View : 9 | Download : 9

Publication Date : 2022-07-16

Article Type : Research Paper

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 , … , x n ] S=k[x1,…,xn] is a polynomial ring over a field, M M is a squarefree monomial ideal in S S , and each minimal generator of M M has degree larger than i i , then pd insert ignore into journalissuearticles values( S / M ); ≤ n − i \pdinsert ignore into journalissuearticles values(S/M);≤n−i .
Keywords : Betti number, free resolution, monomial ideal