Duality of Preenvelopes and Pure Injective Modules

摘要

Let R be an arbitrary ring and let (-)~+ = Homz(-, Q/Z）, where Z is the ring of integers and Q is the ring of rational numbers. Let C be a subcategory of left R-modules and D a subcategory of right R-modules such that X~+ ∈ D for any X ∈C and all modules in C are pure injective. Then a homomorphism f: A → C of left R-modules with C ∈ C is a C-(pre)envelope of A provided f~+: C~+ → A~+ is a D-(pre)cover of A~+. Some applications of this result are given.