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.