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Proceedings of the American Mathematical Society

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

 

 

Lifting up an infinite chain of prime ideals
to a valuation ring


Authors: Byung Gyun Kang and Dong Yeol Oh
Journal: Proc. Amer. Math. Soc. 126 (1998), 645-646
MSC (1991): Primary 13A18; Secondary 13B02
DOI: https://doi.org/10.1090/S0002-9939-98-04063-5
MathSciNet review: 1415329
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that for an arbitrary chain $\{P_\alpha\}$ of prime ideals in an integral domain, there exists a valuation domain which has a chain of prime ideals $\{Q_\alpha\}$ lying over $\{P_\alpha\}$.


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

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  • 2. Irving Kaplansky, Commutative rings, Revised edition, The University of Chicago Press, Chicago, Ill.-London, 1974. MR 0345945
  • 3. Robert Gilmer, Multiplicative ideal theory, Marcel Dekker, Inc., New York, 1972. Pure and Applied Mathematics, No. 12. MR 0427289
    Robert Gilmer, Multiplicative ideal theory, Queen’s Papers in Pure and Applied Mathematics, vol. 90, Queen’s University, Kingston, ON, 1992. Corrected reprint of the 1972 edition. MR 1204267

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Additional Information

Byung Gyun Kang
Affiliation: Department of Mathematics, Pohang University of Science & Technology, Pohang, 790–784, Korea
Email: bgkang@euclid.postech.ac.kr

Dong Yeol Oh
Affiliation: Department of Mathematics, Pohang University of Science & Technology, Pohang, 790–784, Korea

DOI: https://doi.org/10.1090/S0002-9939-98-04063-5
Received by editor(s): May 16, 1996
Received by editor(s) in revised form: July 28, 1996
Additional Notes: This research was supported by the research grant BSRI-95-1431
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 1998 American Mathematical Society