Duality pairs and FP-injective modules over formal triangular matrix rings

Abstract

Suppose that $T=\left(\begin{array}{cc}A& 0\\ U& B\end{array}\right)$ is a formal triangular matrix ring, where A and B are rings and U is a (B, A)-bimodule. We first study how to construct duality pairs of T-modules using duality pairs of A-modules and B-modules. Then we describe the structures of FP-injective left T-modules. Some applications are also given.

Keywords:

• Duality pair
• Formal triangular matrix ring
• FP-injective dimension
• FP-injective module

2010 Mathematics Subject Classification:

• 16D50
• 16D90
• 16E10

Acknowledgements

The author wants to express his gratitude to the referee for the very helpful comments and suggestions.

Additional information

Funding

This research was supported by NSFC (11771202) and Nanjing Institute of Technology of China (CKJA201707, JCYJ201842).