Global ideal theory of meromorphic function fields

Alling, Norman L.

doi:10.1090/S0002-9947-1979-0546917-2

Global ideal theory of meromorphic function fields
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by Norman L. Alling

Trans. Amer. Math. Soc. 256 (1979), 241-266

DOI: https://doi.org/10.1090/S0002-9947-1979-0546917-2

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Abstract:

It is shown that the ideal theories of the fields of all meromorphic functions on any two noncompact Riemann surfaces are isomorphic. Further, various new representation and factorization theorems are proved.

References

Norman L. Alling, The valuation theory of meromorphic function fields over open Riemann surfaces, Acta Math. 110 (1963), 79–96. MR 160781, DOI 10.1007/BF02391855
Norman L. Alling, The valuation theory of meromorphic function fields, Entire Functions and Related Parts of Analysis (Proc. Sympos. Pure Math., La Jolla, Calif., 1966) Amer. Math. Soc., Providence, R.I., 1968, pp. 8–29. MR 0236404
Norman L. Alling, Primary ideals in rings of analytic functions, Proc. Amer. Math. Soc. 53 (1975), no. 2, 423–427. MR 383082, DOI 10.1090/S0002-9939-1975-0383082-0
Bernhard Banaschewski, Zur Idealtheorie der ganzen Funktionen, Math. Nachr. 19 (1958), 136–160 (German). MR 106286, DOI 10.1002/mana.19580190109
Lipman Bers, On rings of analytic functions, Bull. Amer. Math. Soc. 54 (1948), 311–315. MR 24970, DOI 10.1090/S0002-9904-1948-08992-3
Garrett Birkhoff, Lattice Theory, Revised edition, American Mathematical Society Colloquium Publications, Vol. 25, American Mathematical Society, New York, N. Y., 1948. MR 0029876
Herta Florack, Reguläre und meromorphe Funktionen auf nicht geschlossenen Riemannschen Flächen, Schr. Math. Inst. Univ. Münster 1948 (1948), no. 1, 34 (German). MR 37362
Leonard Gillman and Meyer Jerison, Rings of continuous functions, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 0116199, DOI 10.1007/978-1-4615-7819-2
Robert C. Gunning and Hugo Rossi, Analytic functions of several complex variables, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1965. MR 0180696
Olaf Helmer, Divisibility properties of integral functions, Duke Math. J. 6 (1940), 345–356. MR 1851
Melvin Henriksen, On the ideal structure of the ring of entire functions, Pacific J. Math. 2 (1952), 179–184. MR 47928, DOI 10.2140/pjm.1952.2.179
Melvin Henriksen, On the prime ideals of the ring of entire functions, Pacific J. Math. 3 (1953), 711–720. MR 59479, DOI 10.2140/pjm.1953.3.711
Edwin Hewitt, Rings of real-valued continuous functions. I, Trans. Amer. Math. Soc. 64 (1948), 45–99. MR 26239, DOI 10.1090/S0002-9947-1948-0026239-9

On meromorphic function fields on a Stein variety

83

James Kelleher, Rings of meromorphic functions on non-compact Riemann surfaces, Canadian J. Math. 21 (1969), 284–300. MR 240321, DOI 10.4153/CJM-1969-030-3
Simon Kochen, Ultraproducts in the theory of models, Ann. of Math. (2) 74 (1961), 221–261. MR 138548, DOI 10.2307/1970235

Allgemeine Bewertungstheorie

167

O. F. G. Schilling, Ideal theory on open Riemann surfaces, Bull. Amer. Math. Soc. 52 (1946), 945–963. MR 19733, DOI 10.1090/S0002-9904-1946-08669-3
Oscar Zariski and Pierre Samuel, Commutative algebra, Volume I, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, New Jersey, 1958. With the cooperation of I. S. Cohen. MR 0090581

Commutative algebra