Gorenstein flat-cotorsion modules over tensor rings

Let [Formula: see text] be a tensor ring, where [Formula: see text] is a ring and [Formula: see text] is an [Formula: see text]-nilpotent [Formula: see text]-bimodule. Under certain conditions, we characterize the Gorenstein flat-cotorsion modules over [Formula: see text], showing that a [Formula: see text]-module [Formula: see text] is Gorenstein flat-cotorsion if and only if [Formula: see text] is monomorphic and Cokeru is a Gorenstein flat-cotorsion [Formula: see text]-module. As applications, we describe the Gorenstein flat-cotorsion modules over some trivial extension rings and Morita context rings.