Pure projective, pure injective and FP-injective modules over trivial ring extensions

Let [Formula: see text] be a trivial extension of a ring [Formula: see text] by an [Formula: see text]-[Formula: see text]-bimodule [Formula: see text]. We first study the properties of pure projective and pure injective modules over [Formula: see text]. Then we characterize [Formula: see text]-injective modules over [Formula: see text]. Finally some applications are given to Morita context rings.