Show that if $M$ is a closed, connected and orientable manifold, then $M$ is $R-$orientable for any commutative ring $R.$
I got the following hint (Which I do not know how it will help me in the solution):
The advantage of using cohomology than homology is that cohomology have ring structure whch is not found in homology.
Could anyone give me a hint for solving that question please?
