Dual modules, f-projective modules and Π-coherence over trivial ring extensions

Abstract

Let $R⋉M$ be a trivial extension of a ring R by an R-R-bimodule M. We first describe explicitly the structure of a dual module over $R⋉M$. Then we characterize Mittag-Leffler modules and f-projective modules over R × M. Finally, we investigate when $R⋉M$ is a left Π-coherent ring. In addition, some applications are given in formal triangular matrix rings.

KEYWORDS:

• Π-coherent ring
• Dual module
• f-projective module
• formal triangular matrix ring
• trivial extension

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 16D40
• 16D90
• 16P70

Acknowledgments

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 (12271249, 12171230) and NSF of Jiangsu Province of China (BK20211358).