Meromorphic functions and factoriality

Kucharz, W.

doi:10.1090/S0002-9939-05-07748-8

Meromorphic functions and factoriality
HTML articles powered by AMS MathViewer

by W. Kucharz PDF

Proc. Amer. Math. Soc. 133 (2005), 2013-2021 Request permission

Abstract:

Let $K$ be a compact subset of a connected Stein manifold $X$. We study algebraic properties of the ring of meromorphic functions on $X$ without poles in $K$.

References

Hyman Bass, Algebraic $K$-theory, W. A. Benjamin, Inc., New York-Amsterdam, 1968. MR 0249491
Jacek Bochnak, Sur la factorialité des anneaux de fonctions analytiques, C. R. Acad. Sci. Paris Sér. A 279 (1974), 269–272 (French). MR 377100
Jacek Bochnak, Michel Coste, and Marie-Françoise Roy, Real algebraic geometry, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 36, Springer-Verlag, Berlin, 1998. Translated from the 1987 French original; Revised by the authors. MR 1659509, DOI 10.1007/978-3-662-03718-8
N. Bourbaki, Éléments de mathématique. Fascicule XXVII. Algèbre commutative. Chapitre 1: Modules plats. Chapitre 2: Localisation, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1290, Hermann, Paris, 1961 (French). MR 0217051
H. G. 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 333245, DOI 10.1090/S0002-9939-1974-0333245-4
Otto Forster, Zur Theorie der Steinschen Algebren und Moduln, Math. Z. 97 (1967), 376–405 (German). MR 213611, DOI 10.1007/BF01112815
Jacques Frisch, Points de platitude d’un morphisme d’espaces analytiques complexes, Invent. Math. 4 (1967), 118–138 (French). MR 222336, DOI 10.1007/BF01425245
Phillip Griffiths, Topics in algebraic and analytic geometry, Mathematical Notes, No. 13, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1974. Written and revised by John Adams. MR 0355119
Lars Hörmander, An introduction to complex analysis in several variables, Second revised edition, North-Holland Mathematical Library, Vol. 7, North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York, 1973. MR 0344507
Hideyuki Matsumura, Commutative algebra, 2nd ed., Mathematics Lecture Note Series, vol. 56, Benjamin/Cummings Publishing Co., Inc., Reading, Mass., 1980. MR 575344
J. Milnor, On axiomatic homology theory, Pacific J. Math. 12 (1962), 337–341. MR 159327, DOI 10.2140/pjm.1962.12.337
Masahiro Shiota, Geometry of subanalytic and semialgebraic sets, Progress in Mathematics, vol. 150, Birkhäuser Boston, Inc., Boston, MA, 1997. MR 1463945, DOI 10.1007/978-1-4612-2008-4
Yum-tong Siu, Noetherianness of rings of holomorphic functions on Stein compact series, Proc. Amer. Math. Soc. 21 (1969), 483–489. MR 247135, DOI 10.1090/S0002-9939-1969-0247135-7
Richard G. Swan, Vector bundles and projective modules, Trans. Amer. Math. Soc. 105 (1962), 264–277. MR 143225, DOI 10.1090/S0002-9947-1962-0143225-6
Richard G. Swan, Topological examples of projective modules, Trans. Amer. Math. Soc. 230 (1977), 201–234. MR 448350, DOI 10.1090/S0002-9947-1977-0448350-9