2:44 AM
very light error in this theorem in b)
we have to assume that $C/P$ has infinitely small elements for this to be true
equivalently, $P\subseteq M^p$ where $p\not\in\upsilon X$ or ($p\in\upsilon X$ and $P$ is not maximal)
$M^p$ being the maximal ideal corresponding to $p\in\beta X$
