Quasi-Isomorphisms of Commutative DG Rings and Divided Power Structures

We prove that a quasi-isomorphism f : A → B between commutative DGrings, where B admits a divided power structure, can be factored as f = f ̃ ◦ e, wheree : A → B ̃ is a split injective quasi-isomorphism, and f ̃ : B ̃ → B is a surjectivequasi-isomorphism.This result is used in our work on a DG approach to the cotangent complex, and ourwork on the derived category of commutative DG rings.