Which graded commutative $R$-algebras occur as cup product algebras $H^\ast(X;R)$ of spaces $X$?
This is a question in Hatcher's Algebraic Topology (page 214 Chapter 3). Hatcher says that the problem is solved for $R=\mathbb{Q}$ by a paper [Quillen 1969] which I assume is the one titled "Rational Homotopy Theory". Hatcher also says that the case $R=\mathbb{Z}_p$ is also solved for prime $p$. Now where can I find the reference to this? Also, what kind of prerequisites are needed to understand the solution for $R=\mathbb{Q}$ and $R=\mathbb{Z}_p$?
It would also be great if someone directly addresses the solution, just to give an overview. My thanks in advance.