Relative FP-injective modules and relative IF rings

Abstract

Let R be a commutative ring and w be the so-called w-operation on R. Then we introduce and study two concepts of w-FP-injective modules and w-IF rings. To do so, we use two main methods, of which one is to localize at maximal w-ideals of R and the other is to utilize w-Nagata modules over w-Nagata rings. As an application, we characterize Prüfer v-multiplication domains in terms of w-FP-injective modules. Finally we provide an example of a w-IF ring, but not an IF ring using a trivial extension.

Keywords:

• PVMD
• w-copure flat dimension
• w-FP-injective module
• w-IF ring
• w-Nagata module
• w-Nagata ring

2020 Mathematics Subject Classification:

• 13C10
• 13D05
• 13D07
• 13D30

Acknowledgements

The authors thank the referee for careful reading of the manuscript.

Additional information

Funding

This work was partially supported by NSFC (No. 11671283).