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

Author(s): Byung Gyun Kang; Dong Yeol Oh
Journal: Proc. Amer. Math. Soc. 126 (1998), 645-646.
MSC (1991): Primary 13A18; Secondary 13B02
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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 $\{P_\alpha\}$ .

References:

1.: D. D. Anderson, Some Problems in Commutative Ring Theory, Zero-Dimensional Commutative Rings (Lecture Notes in Pure and Applied Mathematics Series/171 edited by D. F. Anderson and D. E. Dobbs), Marcel Decker, New York, 1995. MR 96a:13001
2.: I. Kaplansky, Commutative Rings, The University of Chicago Press, 1974. MR 49:10674
3.: R. Gilmer, Multiplicative Ideal Theory, Marcel Decker, New York, 1972. MR 55:323; MR 93j:13001


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