Abstract
Let R be a ring. A left R-module M is said to be sfp-injective if, for every exact sequence 0 → K → L with K and L super finitely presented left R-modules, the induced sequence Hom(L, M) → Hom(K, M) → 0 is exact. A right R-module N is called sfp-flat if, for every exact sequence 0 → K → L with K and L super finitely presented left R-modules, the induced sequence 0 → N ⊗ K → N ⊗ L is exact. We study precovers and preenvelopes by sfp-injective and sfp-flat modules, including their properties under (almost) excellent extensions of rings
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