Gorenstein and duality pair over triangular matrix rings

Abstract

Let A, B be two rings and T = A M 0 B with M an A-B-bimodule. We first construct a semi-complete duality pair D T of T -modules using duality pairs in A-Mod and B-Mod respectively. Then we characterize when a left T -module is Gorenstein D T -projective, Gorenstein D T -injective or Gorenstein D T -flat. These three class of T -modules will induce model structures on T -Mod. Finally we show that the homotopy category of each of model structures above admits a recollement relative to corresponding stable categories. Our results give new characterizations to earlier results in this direction.

How to construct Gorenstein projective modules relative to complete duality pairs over Morita rings

“…with M ∼ = Ker(P 0 → P 0 ) such that Hom R (P, F ) is exact for any flat left R-module F . For more details on Ding projective modules, we refer to [4,11,21,25,16]. The following is the main result of this section which contains Theorem 1.2 in the introduction.…”