  A differential graded algebra can be viewed as an A-infinity algebra. By a
theorem of Kadeishvili, a dga over a field admits a quasi-isomorphism from a
minimal A-infinity algebra. We introduce the notion of a derived A-infinity
algebra and show that any dga A over an arbitrary commutative ground ring k is
equivalent to a minimal derived A-infinity algebra. Such a minimal derived
A-infinity algebra model for A is a k-projective resolution of the homology
algebra of A together with a family of maps satisfying appropriate relations.
  As in the case of A-infinity algebras, it is possible to recover the dga up
to quasi-isomorphism from a minimal derived A-infinity algebra model. Hence the
structure we are describing provides a complete description of the
quasi-isomorphism type of the dga.

K-Theory and Homology;Algebraic Topology;Rings and Algebras