|
Meromorphic functions and factoriality
Author(s):
W.
Kucharz
Journal:
Proc. Amer. Math. Soc.
133
(2005),
2013-2021.
MSC (2000):
Primary 32A20, 32A38
Posted:
January 14, 2005
MathSciNet review:
2137867
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
Let be a compact subset of a connected Stein manifold . We study algebraic properties of the ring of meromorphic functions on without poles in .
References:
-
- [1]
- H. Bass, Algebraic
-Theory, New York, Benjamin, 1968. MR 0249491 (40:2736) - [2]
- J. Bochnak, Sur la factorialité des anneaux de fonctions analytiques, C. R. Acad. Sci. Paris Sér. A 279 (1974), 269-272. MR 0377100 (51:13274)
- [3]
- J. Bochnak, M. Coste and M.-F. Roy, Real Algebraic Geometry, Ergebnisse der Math. und ihrer Grenzgeb. Folge 3, Vol. 36, Berlin Heidelberg New York, Springer, 1998. MR 1659509 (2000a:14067)
- [4]
- N. Bourbaki, Algèbre Commutative, Paris, Hermann, 1961-1965. MR 0217051 (36:146); MR 0171800 (30:2027); MR 0194450 (33:2660); MR 0260715 (41:5339)
- [5]
- H. Dales, The ring of holomorphic functions on a Stein compact set as a unique factorization domain, Proc. Amer. Math. Soc. 44 (1974), 88-92. MR 0333245 (48:11570)
- [6]
- O. Forster, Zur Theorie der Steinschen Algebren und Moduln, Math. Z. 97 (1967), 376-405. MR 0213611 (35:4469)
- [7]
- J. Frisch, Points de platitude d'un morphisme d'espaces analytiques complexes, Invent. Math. 4 (1967), 118-138. MR 0222336 (36:5388)
- [8]
- P. Griffiths and J. Adams, Topics in Algebraic and Analytic Geometry, Math. Notes, Vol. 13, Princeton Univ. Press, Princeton, New Jersey, 1974. MR 0355119 (50:7596)
- [9]
- L. Hörmander, An Introduction to Complex Analysis in Several Variables, Second edition, North-Holland Publishing Comp., 1979. MR 0344507 (49:9246)
- [10]
- H. Matsumura, Commutative Algebra, Second edition, Math. Lecture Note Series 56, Benjamin/Cummings, London Amsterdam Tokyo, 1980. MR 0575344 (82i:13003)
- [11]
- J. Milnor, On axiomatic homology theory, Pacific J. Math. 12 (1962), 337-341. MR 0159327 (28:2544)
- [12]
- M. Shiota, Geometry of Subanalytic and Semialgebraic Sets, Birkhäuser, Boston Basel Berlin, 1997. MR 1463945 (99b:14061)
- [13]
- Y.-T. Siu, Noetherianness of rings of holomorphic functions on Stein compact series, Proc. Amer. Math.
Soc. 21 (1969), 483-489. MR 0247135 (40:404) - [14]
- R. Swan, Vector bundles and projective modules, Trans. Amer. Math. Soc. 105 (1962), 264-277. MR 0143225 (26:785)
- [15]
- R. Swan, Topological examples of projective modules, Trans. Amer. Math. Soc. 230 (1977), 201-234. MR 0448350 (56:6657)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (2000):
32A20, 32A38
Retrieve articles in all Journals with
MSC (2000):
32A20, 32A38
Additional Information:
W.
Kucharz
Affiliation:
Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany -- and -- Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131-1141
Email:
kucharz@math.unm.edu
DOI:
10.1090/S0002-9939-05-07748-8
PII:
S 0002-9939(05)07748-8
Received by editor(s):
April 17, 2003
Received by editor(s) in revised form:
February 26, 2004
Posted:
January 14, 2005
Additional Notes:
This paper was written at the Max-Planck-Institut für Mathematik in Bonn, whose support and hospitality are gratefully acknowledged
Communicated by:
Michael Stillman
Copyright of article:
Copyright
2005,
American Mathematical Society
|