then for any open set U of X, ρ(A) spans F(U) as an OU-module. Here
is the restriction map. In words, all sections of F are locally generated by the global sections.
An example of such a sheaf is that associated in algebraic geometry to an R-module M, R being any commutative ring, on the spectrum of a ring Spec(R). Another example: according to Cartan's theorem A, any coherent sheaf on a Stein manifold is spanned by global sections.