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Kaplansky's problem on valuation rings


Authors: László Fuchs and Saharon Shelah
Journal: Proc. Amer. Math. Soc. 105 (1989), 25-30
MSC: Primary 13L05; Secondary 03C60, 03E35, 13A18
DOI: https://doi.org/10.1090/S0002-9939-1989-0929431-3
MathSciNet review: 929431
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Abstract | References | Similar Articles | Additional Information

Abstract: The following theorem is proved in ZFC: there exist valuation rings which are not surjective homomorphic images of valuation domains. The proof relies on the existence of nonstandard divisible uniserial modules in ZFC.


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

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1989-0929431-3
Keywords: Valuation rings, valuation domains, uniserial, divisible modules, nonstandard uniserials, first order model, ZFC, forcing
Article copyright: © Copyright 1989 American Mathematical Society

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