Abstract: Let A/S be a Frobenius extension of rings with S coherent and C a semidualizing S-module. Firstly, we prove that G_C-flatness with respect to a semidualizing module is invariant under Frobenius extensions by using the construction method, that is, for an A-module M, M_A is G_CSA-flat module if and only if M_S is G_C-flat. Secondly,  we prove that G_C-flat dimension with respect to a semidualizing module is preserved under Frobenius extensions.

Key words: semidualizing module, G_C-flat module, G_C-flat dimension, Forbenius extension