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.
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