Rational cohomology of an integral Eilenberg–MacLane space
= Rational cohomology of an integral Eilenberg–MacLane space
{title2=$H^*(K(\mathbb Z,n);\mathbb Q)$}
The ring is exterior on its degree-$n$ universal class for odd $n$, and polynomial for even $n$. The path-loop <Serre spectral sequence> alternates these two types by transgression. In the polynomial-fiber case its derivation has nonzero coefficients $k$ on powers, which become invertible over the rationals.