Differential graded algebras, or DGAs, are a basic object of study in many areas of modern mathematics. While they were present (implicitly at least) since the start of modern differential geometry, I would like to know where the abstract definition of a DGA was first written down, and by whom?



Who introduced the abstract definition of a DGA?
Search for the earliest appearance of "differential graded algebra" and "DGA" on MathSciNet. The earliest hit is DGA in a review of a 1954 paper of Cartan where DGA (or more precisely, the redundant term "DGA-algebra") is defined: "Sur les groupes d'Eilenberg-Mac Lane $H(\Pi,n)$ I. Méthode des constructions," Proc. Nat. Acad. Sci. U.S.A. 40 (1954), 467–471. In the same year there is an entry from the Cartan seminar: Séminaire Henri Cartan de l'Ecole Normale Supérieure, 1954/1955. Algèbres d'Eilenberg-MacLane et homotopie.


