Relative Gorenstein flat modules and dimension

Abstract

In this article, the new concept of relative Gorenstein flat modules is introduced. We give a survey of their behavior in terms of both structural and dimension properties. We relate the class consisting of all these new modules to those of classical Gorenstein flat modules and of relative Gorenstein injective modules, and we compare the corresponding homological dimensions. This treatment includes the study of relative strongly Gorenstein flat modules as an important and structural part of relative Gorenstein flat modules. We also tackle the classical problem of the stability of the Gorenstein condition under iterations of its construction.

Keywords:

• Relative Gorenstein dimensions
• relative (strongly) Gorenstein modules
• weakly Wakamatsu tilting modules

2020 Mathematics Subject Classification:

• Primary: 16E10
• Secondary: 16E65

Acknowledgment

The authors would like to thank the referee for the careful reading of this paper and the valuable comments.

Additional information

Funding

This research was partially supported by the grant PID2020-113552GB-I00 from Ministerio de Ciencia e Innovación and the grant P20-00770 from Junta de Andalucía.