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Proceedings of the American Mathematical Society
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
MathSciNet review: 1415329
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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 $\{P_\alpha\}$.


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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: http://dx.doi.org/10.1090/S0002-9939-98-04063-5
PII: S 0002-9939(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