Duality Pairs Induced by One-Sided Gorenstein Subcategories

Abstract

For a ring R and an additive subcategory C of the category Mod R of left R-modules, under some conditions we prove that the right Gorenstein subcategory of Mod R and the left Gorenstein subcategory of Mod R op relative to C form a coproduct-closed duality pair. Let R, S be rings and C a semidualizing (R, S)-bimodule. As applications of the above result, we get that if S is right coherent and C is faithfully semidualizing, then (GF C (R), GI C (R op )) is a coproduct-closed duality pair and GF C (R) is covering in Mod R, where GFC (R) is the subcategory of Mod R consisting of C-Gorenstein flat modules and GIC(R op ) is the subcategory of Mod R op consisting of C-Gorenstein injective modules; we also get that if S is right coherent, then (AC(R op ), lG(FC(R))) is a coproductclosed and product-closed duality pair and AC (R op ) is covering and preenveloping in Mod R op , where AC (R op ) is the Auslander class in Mod R op and lG(FC (R)) is the left Gorenstein subcategory of Mod R relative to C-flat modules.