FILTERED-INJECTIVE AND COFLAT MODULES

Abstract

For an arbitrary left R-module M, we denote by F(M) the class of left R-modules F such that for any exact sequence 0 → A α→ B of left R-modules and any R-homomorphism β: A → M factoring through F, there exists an R- homomorphism γ: B → M such that β = γα. For any given class R of left R-modules, we denote _∩EϵR F(M) by F(R) or simply by 9 if the context is clear. The class of short exact sequences E of left R-modules relative to which each ME'JR has the injective property, is denoted by E(R) or just &. Relative properties of RR, F and E are investigated for a given class R. The special case where JR is the class of all pure-injective left R-modules is explored. In this way the class F of coflat left R-modules is introduced and it is pointed out that a module is coflat if and only if it is absolutely pure.