Let R and S be rings,SMR be a Frobenius bimodule with generator MR.Let X be a class of left R-modules and y a class of left S-modules.Under some conditions,it was proved that a left R-module X is n-X-Gorenstein projective if and only if M⊗RX is a n-y-Gorenstein projective left S-module.We also proved that if F:RM→SMis a faithful Frobenius functor,then n-Gx-pdR(X)=n-Gy-pds(F(X)).
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