Generalized Gorenstein modules with respect to duality pairs over triangular matrix rings

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]. Finally, we construct model structures and recollements relative to these generalized Gorenstein modules.