In this paper, we introduce two new classes of modules called SFI-injective and SFI-flat modules, we give their characterizations and we study the effect of these classes over exact sequences. Then we show that a ring R is Quasi-Frobenius (resp., IF) if and only if every module is SFI-injective (resp., SFI-flat). An example is given to show that SFI-injective (resp., SFI-flat) is not identical with injective (resp., flat) module. Also, we discuss when the homomorphic image of an SFI-injective module is SFI-injective and when the submodule of an SFI-flat module is SFI-flat.

SFI-injective module, SFI-flat module, FI-injective module, FI-flat module, strongly FP-injective module, FP-injective module, Quasi-Frobenius ring, IF ring.