Syzygies of the residue field over Golod rings

Doan Trung Cuong, Hailong Dao, David Eisenbud, Toshinori Kobayashi, Claudia Polini, Bernd Ulrich

Published 2024-08-24Version 1

Let $(R,m,k)$ be a Golod ring. We show a recurrent formula for high syzygies of $k$ interms of previous ones. In the case of embedding dimension at most $2$, we provided complete descriptions of all indecomposable summands of all syzygies of $k$.