  We describe the cohomology of the quotient Z_K/H of a moment-angle complex
Z_K by a freely acting subtorus H in T^m by establishing a ring isomorphism of
H*(Z_K/H,R) with an appropriate Tor-algebra of the face ring R[K], with
coefficients in an arbitrary commutative ring R with unit. This result was
stated in [BP02, 7.37] for a field R, but the argument was not sufficiently
detailed in the case of nontrivial H and finite characteristic. We prove the
collapse of the corresponding Eilenberg-Moore spectral sequence using the
extended functoriality of Tor with respect to `strongly homotopy
multiplicative' maps in the category DASH, following Munkholm [Mu74]. Our
collapse result does not follow from the general results of Gugenheim-May and
Munkholm.
