Cohomology rings of multiplicative fibrations

Let p be an odd prime. Let be the fibre space induced from an H-map where K is a generalized Eilenberg MacLane space and X is a simply connected H-space. Such spaces occur frequently in Postnikov towers and connective covers. In this paper, we compute the mod p cohomology of as a ring. The ring depends on the structure of imf* and the structure of subkerf* as modules over the Steenrod algebra.