$D_\infty$-differential $E_\infty$-algebras and multiplicative spectral sequences

The concept of $D_\infty$-differential $E_\infty$-algebra is introduced, which is a homotopy-invariant deformation analogue of the concept of $E_\infty$-algebra. The main homotopy properties of $D_\infty$-differential $E_\infty$-algebras are studied and relations between $D_\infty$-differential $E_\infty$-algebras and multiplicative spectral sequences over fields are established.