• Endliche Erzeugbarkeit im Ring...

Result: Endliche Erzeugbarkeit im Ring aller holomorphen Funktionen

Title:
Endliche Erzeugbarkeit im Ring aller holomorphen Funktionen
Authors:
LANGMANN, Klaus
Source:
Manuscripta Mathematica. 19:375-383
Publisher Information:
Springer Science and Business Media LLC, 1976.
Publication Year:
1976
Subject Terms:
510.mathematics, Analytic sheaves and cohomology groups, 4. Education, Analytic subsets and submanifolds, 0103 physical sciences, Stein spaces, 0101 mathematics, 16. Peace & justice, 01 natural sciences, Article, Algebras of holomorphic functions of several complex variables
Document Type:
Academic journal Article
File Description:
application/xml; image/jpeg; application/pdf
Language:
German
ISSN:
1432-1785
0025-2611
DOI:
10.1007/bf01278925
Access URL:
https://zbmath.org/3549354
https://doi.org/10.1007/bf01278925
https://link.springer.com/article/10.1007/BF01278925
Rights:
Springer TDM
Accession Number:
edsair.doi.dedup.....a8601c2d865f8e01e34a58a9d15f62e9
Database:
OpenAIRE

Further Information

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.