Doan Trung Cuong

collaborators

3 papers

math.AC2026

On the pertubations of E-depth, Ef-depth and sequentially Cohen-Macaulay locus

Doan Trung Cuong, Le Thanh Nhan, Nguyen Xuan Linh

Let (R,m) be a Noetherian local ring, I an ideal of R and M a finitely generated R-module. In this paper, we define and study E-depth and Ef-depth of M in I. We prove that E-depth…

math.AC2025

On direct summands of syzygies of the residue field of a local ring

Doan Trung Cuong, Toshinori Kobayashi

We investigate local rings in which a syzygy of the residue field occurs as a direct summand of another syzygy of the field. This class of local rings includes Golod rings, Burch r…

math.AC2025

Syzygies of the residue field over Golod rings

Doan Trung Cuong, Hailong Dao, David Eisenbud +3

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 d…