Abstract
Let 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 . Then we characterize Mittag-Leffler modules and f-projective modules over R × M. Finally, we investigate when is a left Π-coherent ring. In addition, some applications are given in formal triangular matrix rings.
Acknowledgments
The author wants to express his gratitude to the referee for the very helpful comments and suggestions.