Gorenstein Flat Covers of Modules over Gorenstein Rings Original Research Article

A left and right Noetherian ringRis called Gorenstein if bothRRandRRhave finite injective dimensions. These rings were studied by Bass for the commutative case and Iwanaga for the noncommutative case. In this paper, we define Gorenstein flat modules over a Gorenstein ring. These modules are a generalization of flat modules. After discussing the properties of modules over a Gorenstein ring, we prove that every module over a Gorenstein ring has a Gorenstein flat cover or a minimal right approximation by a Gorenstein flat module in Auslander and Reitenʹs terminology.