WEAK GORENSTEIN PROJECTIVE, INJECTIVE AND FLAT MODULES

Abstract

In this paper, weak Gorenstein projective, injective and flat modules are introduced and investigated. A left R-module M is called weak Gorenstein projective if there exists an exact sequence ⋯ → P1 → P0 → P0 → P1 → ⋯ of left R-modules such that: (1) all Pi and Pi are projective; and (2) M ≅ ker (P0 → P1). The weak Gorenstein injective and flat modules are defined similarly. Several well-known classes of rings are characterized in terms of weak Gorenstein projective, injective and flat modules. We also give a partial answer to Holm's question ([Question C, on p. 114 in Gorenstein projective, injective and flat modules, MSc thesis, Institute for Mathematical Sciences, University of Copenhagen (2000)]).