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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
MathSciNet review: 929431
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0929431-3
PII: S 0002-9939(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