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Algebra Comput."],"published-print":{"date-parts":[[2024,3]]},"abstract":"<jats:p> Let A and B be rings and [Formula: see text] with M an A-B-bimodule. We first construct a semi-complete duality pair [Formula: see text] over T using duality pairs over A and B, respectively. Then we characterize when a left T-module is Gorenstein projective, injective or flat with respect to the duality pair [Formula: see text]. As applications, we investigate when a left T-module is projectively coresolved Gorenstein flat, Ding injective or Gorenstein flat. In addition, we give an estimate of Gorenstein flat dimension of a left T-module with respect to [Formula: see text]. 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