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We prove that a quasi-isomorphism $f : A \to B$ between commutative DG rings,where $B$ admits a divided power structure, can be factored as $f = \tilde{f}\circ e$, where $e : A \to \tilde{B}$ is a split injective quasi-isomorphism,and $\tilde{f} : \tilde{B} \to B$ is a surjective quasi-isomorphism.  This result is used in our work on a DG approach to the cotangent complex,and our work on the derived category of commutative DG rings.

Quasi-Isomorphisms of Commutative DG Rings and Divided Power Structures