Some counterexamples related to integral closure in $D[[x]]$
HTML articles powered by AMS MathViewer
- by Jack Ohm
- Trans. Amer. Math. Soc. 122 (1966), 321-333
- DOI: https://doi.org/10.1090/S0002-9947-1966-0202753-9
- PDF | Request permission
References
- N. Bourbaki, ĂlĂ©ments de mathĂ©matique. Fasc. XXX. AlgĂšbre commutative. Chapitre 5: Entiers. Chapitre 6: Valuations, ActualitĂ©s Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1308, Hermann, Paris, 1964 (French). MR 0194450
- Robert Gilmer and Jack Ohm, Integral domains with quotient overrings, Math. Ann. 153 (1964), 97â103. MR 159835, DOI 10.1007/BF01361178
- Robert Gilmer and Jack Ohm, Primary ideals and valuation ideals, Trans. Amer. Math. Soc. 117 (1965), 237â250. MR 169871, DOI 10.1090/S0002-9947-1965-0169871-4
- Melvin Henriksen, On the ideal structure of the ring of entire functions, Pacific J. Math. 2 (1952), 179â184. 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), 711â720. MR 59479, DOI 10.2140/pjm.1953.3.711
- Paul Jaffard, Les systĂšmes dâidĂ©aux, Travaux et Recherches MathĂ©matiques, IV, Dunod, Paris, 1960 (French). MR 0114810
- Wolfgang Krull, Ăber die Zerlegung der Hauptideale in allgemeinen Ringen, Math. Ann. 105 (1931), no. 1, 1â14 (German). MR 1512701, DOI 10.1007/BF01455805 â, Allgemeine Bewertungstheorie, J. Reine Angew. Math. 167 (1931), 160-196. â, Beitrage zur Arithmetik kommutativer Integritatsbereiche. I, Math. Z. 41 (1936), 544-577.
- Wolfgang Krull, BeitrĂ€ge zur Arithmetik kommutativer IntegritĂ€tsbereiche, Math. Z. 41 (1936), no. 1, 665â679 (German). MR 1545646, DOI 10.1007/BF01180447
- Masayoshi Nagata, Local rings, Interscience Tracts in Pure and Applied Mathematics, No. 13, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0155856 T. Nakayama, On Krullâs conjecture concerning completely integrally closed integrity domains. I, Proc. Imp. Acad. Tokyo 18 (1942), 185-187; II, Proc. Imp. Acad. Tokyo 18 (1942), 233-236; III, Proc. Japan Acad. 22 (1946), 249-250.
- P. Ribenboim, Sur une conjecture de Krull en thĂ©orie des valuations, Nagoya Math. J. 9 (1955), 87â97 (French). MR 73586, DOI 10.1017/S002776300002331X
- P. Ribenboim, Anneaux normaux rĂ©els Ă caractĂšre fini, Summa Brasil. Math. 3 (1956), 213â253 (French). MR 97391 P. Samuel, MĂ©chants anneaux de sĂ©ries formelles, J. dâAlgĂšbre, Univ. de Clermont, Polycopied notes, 1963, 1-5.
- Gerhard Schiffels, Graduierte Ringe und Moduln, Bonn. Math. Schr. 11 (1960), xi+122 (German). MR 125134
- A. Seidenberg, Derivations and integral closure, Pacific J. Math. 16 (1966), 167â173. MR 188247, DOI 10.2140/pjm.1966.16.167
- 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 â, Commutative algebra, Vol. II, Van Nostrand, New York, 1961.
Bibliographic Information
- © Copyright 1966 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 122 (1966), 321-333
- MSC: Primary 13.80; Secondary 13.93
- DOI: https://doi.org/10.1090/S0002-9947-1966-0202753-9
- MathSciNet review: 0202753