I am trying to learn about the Eilenberg-Moore spectral sequence to compute homology and cohomology. I have been using Hatcher's book on spectral sequences and also McCleary's "A User's Guide to Spectral Sequences" but I am confused about the convergence of the sequence if we take coefficients in a ring, such as the integers, rather than a field. The two texts seem to use coefficients over a field.
Does the spectral sequence converge if we take ring coefficients?