I'm studying on "Cohen-Macaulay rings" of Bruns-Herzog, here a link:
http://books.google.co.in/books?id=ouCysVw20GAC&printsec=frontcover&hl=it#v=onepage&q&f=false
At page 65 there is the Auslander-Buchsbaum_serre theorem, I need help on one implication:
Let $(R,\mathfrak{m},k)$ be a Noetherian local ring then if $\mathrm{proj\;dim}\;k<\infty$ then $R$ is regular. For this implication the book says that it uses the Ferrand-Vasconcelos theorem:
Let $(R,\mathfrak{m})$ be a Noetherian local ring, and $I\neq0$ a proper ideal with $\mathrm{proj\;dim}\;I<\infty$. If $I/I^2$ is a free $R/I$-module, the $I$ is generated by a regular sequence.
I didn't understand how we apply Ferrand-Vasconcelos, could you help me please?