Abstract
Let [Formula: see text] be a Morita ring with [Formula: see text]. We first study how to construct (complete) duality pairs of [Formula: see text]-modules using (complete) duality pairs of [Formula: see text]-modules and [Formula: see text]-modules, generalizing the result of Mao (Commun. Algebra 12 (2020) 5296–5310) about the duality pairs over a triangular matrix ring. Moreover, we construct Gorenstein projective modules relative to complete duality pairs of [Formula: see text]-modules. Finally, we give an application to Ding projective modules.
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