Weak Gorenstein Cotorsion Modules

Abstract

Let R be a ring and let 𝒮𝒢ℱ be the class of strongly Gorenstein at right R-modules. We call a right R-module M a weak Gorenstein cotorsion module if M is in the class 𝒮𝒢ℱ⊥. Properties of weak Gorenstein cotorsion modules are investigated. It is shown that weak Gorenstein cotorsion R-modules over coherent rings are indeed weaker than Gorenstein cotorsion R-modules. Weak Gorenstein cotorsion dimension for modules and rings are also studied.