Guocheng Dai

activity

20212026

collaborators

5 papers

math.AC2026

Direct products of Gorenstein flat modules over coherent rings

Guocheng Dai, Jiangsheng Hu

We construct a commutative coherent local algebra of Krull dimension zero and a countably generated projectively coresolved Gorenstein flat module whose countable power has infinit…

math.AC2026

Baer Splitting Beyond $τ_{q}$ -Semisimplicity

Xiaolei Zhang, Guocheng Dai

For a commutative ring $R$ , we call an $R$ -module $B$ Baer if $\Ext_R^1(B,T)=0$ for torsion $R$ -module $T$ . It is known that every Baer module is projective when $R$ is $τ_{q}$ -semis…

math.RA2026

Mittag-Leffler Conditions, Gorenstein Modules and Homological Invariants

Guocheng Dai, Xiaolei Zhang

In this paper, we investigate certain properties on the Mittag-Leffler conditions via set-theoretic methods. We establish that a strongly $ℵ_{1}$ -presented module $M$ satisfying…

math.AC2022

Some remarks on Lucas modules

Xiaolei Zhang, Guocheng Dai, Wei Qi

In this paper, we discuss some properties on Lucas modules. In details, we show that direct and inverse limits of Lucas modules are Lucas modules, and every $R$ -module has a Lucas…

math.AC2021

Semi-regular flat modules over strong Prüfer rings

Xiaolei Zhang, Guocheng Dai, Xuelian Xiao +1

We first introduce and study the notion of semi-regular flat modules, and then show that a ring $R$ is a strong \Prufer\ ring if and only if every submodule of a semi-regular flat…