Endliche Erzeugbarkeit im Ring aller holomorphen Funktionen

Abstract

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