Cohomology rings of multiplicative fibrations

Let p be an odd prime. Let X ˜ be the fibre space induced from an H-map f : X → K 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 X ˜ as a ring. The ring depends on the structure of im f * and the structure of subker f * as modules over the Steenrod algebra.