Endliche Erzeugbarkeit im Ring aller holomorphen Funktionen

Let G be a compact Stein set having structure sheafO and define R=(G,O). If , is a coherent sheaf, we consider M=(G,). Then we have following theorem: A submodule NM is finitely generated iff for every infinite set A Boundary G there exists a infinite subset BA and a coherent subsheafN such thatN _z=NO _z for every zB. From this results a short algebraic proof of Frisch's theorem.