Minimal free resolution of a graded ideal with linear quotients

Abstract

Let I be a graded ideal of K[x 1 , . . . , x n ] generated by homogeneous polynomials of a same degree d, and assume that I has linear quotients. In this note, we use Horseshoe Lemma to give a relatively direct inductive construction of a minimal free resolution of I, which is called a d-linear resolution.