Gorenstein AC-graded Flat Modules

This paper mainly studies some homological properties of Gorenstein AC-graded flat modulesFirstly,graded absolutely clean and graded level modules are introduced and some properties of them are given.Secondly,we introduce the concept of Gorenstein AC-graded flat modules and prove that the class of Gorenstein graded flat modules is projectively resolving if and only if it is closed under extension.We also introduce the concept of left graded GFac-closed rings,some properties of Gorenstein AC-graded flat modules over this graded ring are given.We also discuss the existence of Gorenstein AC-graded flat covers.Finally,we consider the stability of the class of Gorenstein AC-graded flat modules,that is we show that gr-(?)Fac(R)=gr-(?)2Fac(R).