N-Ding Projective Modules Over Frobenius Extensions Of Rings

In this paper,we discuss the Ding projective and n-Ding projective modules over(separable)Frobenius extensions of rings.Firstly,we investigate projective,injective,flat and FP-injective modules and dimensions over(separable)Frobe-nius extensions of rings.Secondly,investigate Ding projective modules and Ding projective dimensions over(separable)Frobenius extensions of rings.Finally,we in-troduce the definition of n-Ding projective modules,and study the n-Ding projective modules over Frobenius extensions of rings.Let R(?)A be a separable Frobenius extension,and let M be any left A-module,we prove that M is n-Ding projective left A-module if and only if M is n-Ding projective left R-module if and only if A(?)R M(HomR(A,M))are n-Ding projective left A-modules.Furthermore,we get some conclusions on n-Ding projective dimensions.