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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On a conjecture regarding nonstandard uniserial modules


Authors: Paul C. Eklof and Saharon Shelah
Journal: Trans. Amer. Math. Soc. 340 (1993), 337-351
MSC: Primary 13C13; Secondary 03E35, 03E75, 13A18, 13L05
MathSciNet review: 1159192
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Abstract: We consider the question of which valuation domains (of cardinality $ {\aleph _1}$) have nonstandard uniserial modules. We show that a criterion conjectured by Osofsky is independent of $ {\text{ZFC}} + {\text{GCH}}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1993-1159192-2
PII: S 0002-9947(1993)1159192-2
Keywords: Valuation domain, uniserial, nonstandard uniserial, Axiom$ (S)$, Gamma invariant
Article copyright: © Copyright 1993 American Mathematical Society