Mod-two cohomology ring of real projective space
= Mod-two cohomology ring of real projective space
{title2=$H^*(\mathbb{RP}^m;\mathbb F_2)$}
The mod-two cohomology ring of real projective space is
$$
H^*(\mathbb{RP}^m;\mathbb F_2)\cong\mathbb F_2[y]/(y^{m+1}),
\qquad |y|=1.
$$