n-Gorenstein Projective Modules and Dimensions over Frobenius Extensions

In this paper, we study n-Gorenstein projective modules over Frobenius extensions and n-Gorenstein projective dimensions over separable Frobenius extensions. Let R ? A be a Frobenius extension of rings and M any left A-module. It is proved that M is an n-Gorenstein projective left A-module if and only if A ?;M and Hom;（A, M） are n-Gorenstein projective left A-modules if and only if M is an n-Gorenstein projective left R-module. Furthermore, when R ? A is a separable Frobenius extension, n-Gorenstein projective dimensions are considered.