The Forster–Swan theorem is a result from commutative algebra that states an upper bound for the minimal number of generators of a finitely generated module
over a commutative Noetherian ring.
The usefulness of the theorem stems from the fact, that in order to form the bound, one only need the minimum number of generators of all localizations
The theorem was proven in a more restrictive form in 1964 by Otto Forster[1] and then in 1967 generalized by Richard G. Swan[2] to its modern form.
Let According to Nakayama's lemma, in order to compute
Define the local