The coalgebra structure of the cohomology of multiplicative fibrations

Let p be an odd prime. Let X be a simply connected H-space and let K   be a generalized Eilenberg–MacLane space. Let X˜ be the fibre space induced from an H  -map f:X→Kf:X→K. Then X˜ inherits an H  -structure and there is a multiplicative fibration ΩKX˜X. The cohomology ring H⁎(X˜;Zp) is computed in Lin (2009) [4]. In this note, we examine the coalgebra structure of H⁎(X˜;Zp). We prove there is a choice of algebra generators for H⁎(X˜;Zp) with reduced coproduct in imρ⁎⊗imρ⁎.