Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

The ring of holomorphic functions on a Stein compact set as a unique factorization domain


Author: H. G. Dales
Journal: Proc. Amer. Math. Soc. 44 (1974), 88-92
MSC: Primary 32E25
DOI: https://doi.org/10.1090/S0002-9939-1974-0333245-4
MathSciNet review: 0333245
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ \Gamma $ be the ring of germs of analytic functions on a Stein compact subset $ K$ of a complex-analytic space. Necessary and sufficient conditions on $ K$ for $ \Gamma $ to be a unique factorization domain are given.


References [Enhancements On Off] (What's this?)

  • [1] H. Cartan, Variétés analytiques réelles et variétés analytiques complexes, Bull. Soc. Math. France 85 (1957), 77-99. MR 20 #1339. MR 0094830 (20:1339)
  • [2] J. Frisch, Points de platitude d'un morphisme d'espaces analytiques complexes, Invent. Math. 4 (1967), 118-138. MR 36 #5388. MR 0222336 (36:5388)
  • [3] R. C. Gunning and H. Rossi, Analytic functions of several complex variables, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Englewood Cliffs, N.J., 1965. MR 31 #4927. MR 0180696 (31:4927)
  • [4] I. Kaplansky, Commutative rings, Allyn and Bacon, Boston, Mass., 1970. MR 40 #7234. MR 0254021 (40:7234)
  • [5] Y.-T. Siu, Noetherianness of rings of holomorphic functions on Stein compact subsets, Proc. Amer. Math. Soc. 21 (1969), 483-489. MR 40 #404. MR 0247135 (40:404)
  • [6] -, Hilbert Nullstellensatz in global complex-analytic case, Proc. Amer. Math. Soc. 19 (1968), 296-298. MR 36 #5391. MR 0222339 (36:5391)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 32E25

Retrieve articles in all journals with MSC: 32E25


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0333245-4
Keywords: Analytic space, germs of analytic functions, Stein compact set, Noetherian ring, unique factorization domain
Article copyright: © Copyright 1974 American Mathematical Society

American Mathematical Society