## Cohomology ring of RPn\mathbb RP^n with integral coefficient.

I know cup product structure on H∗(RPn;Z2)=Z2[α]/(αn+1). How to get H∗(RPn;Z) from this? I have two cochain complexes for two coefficient rings. Now my question is what will be the induced map between these two cochain complexes and what will be H∗(RPn;Z)? Answer I think, H∗(RP2n+1)=Z[α,β]/(2α,αn+1,αβ,β2), where α has degree 2 and β has degree … Read more