Abstract :
Let A be a commutative ring and M be a projective module of rank k with n generators. Let h = n−k. Standard computations show that M becomes free after (n choose k)
localizations in comaximal elements.
When the base ring contains a field with at least hk+2 elements we construct a comaximal family G with at most (hk+1)(nk+1) elements such that
for each g in G, the module M[1/g] is free over A[1/g] .
Résumé :