Page "Projective module" Paragraph 52

Let P be a finitely generated projective module over a commutative ring R and X be the spectrum of R. The rank of P at a prime ideal in X is the rank of the free-module.

It is a locally constant function on X.

In particular, if X is connected ( that is if R or its quotient by its nilradical is an integral domain ), then P has constant rank.