Proof: Every R-module being projective implies every short exact sequence 0→D→M→N→0 splits since N is an R-module and thus projective, therefore arbitrary D is also injective. Likewise, if every R-module is injective, then for an arbitrary R-module D we have 0→L→M→D→0 splits as L is injective, so that D is projective. ◻
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