Let $A$ be a noetherian regular local ring of dimension $n$, and $P\subset A$ a prime ideal, such that $A/P$ still a regular local ring of dimension $m$.
I want to show $P/P^2$ is a $n-m$ rank free module over $A/P$.
I am reading Hartshorne recently. When I learn "Differentials", I think the answer is yes, but I have a bad command for commutative algebra. I have learned Atiyah before but I can't work it out. Could someone give it a proof or some relative references? Thanks a lot.
