There are three basic constructions in literature which relate a 1-connected topological space X to a differential graded algebra. Adams and Hilton [2] constructed a chain algebra (with integer coefficients) for the loop space ~?X, a special version of which is Adams' cobar construction [1]. Later Quillen [13] associated a differential graded rational Lie algebra 2(X) to the space X, and Sullivan [14,15], using simplicial differential forms with rational coefficients, obtained a DG commutative cochain algebra for X. For these cochain algebras, Sullivan introduces the notion of minimal model, which corresponds to the Postnikov decomposition of a space.In this paper, we construct minimal models for chain algebras (over any field) and for rational DG Lie algebras. These minimal models correspond to the Eckmann-Hilton homology decomposition of a space. The algebraic construction of the minimal model uses algebraic versions of the Hurewicz and BlakersMassey theorems (2.6), (2.9). The corresponding minimal models for topological spaces are studied in § 3. § 0. Recollection of Notations and ResultsOur references for notations are [10] and [13]. For the reader's convenience, we here collect basic definitions and facts we shall use in this paper.

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