# Eilenberg-Moore Spectral Sequence for Homology with Coefficients in the Integers

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?

• maybe the problem is not the convergence, but rather that we do not have an isomorphism: $$\bigoplus_{p+q=n} E^r_{p, q} \sim H_n(E)$$ where $E$ is the total space of some fibration, the coefficients are in the relevant ring, and $r$ is sufficiently large. In case the ring is a field, we always have such isomorphism, if the sequence converges – fritz Jan 31 '17 at 15:21