Kaplansky's Problem on Valuation Rings

DOI10.2307/2046728zbMath0691.13027OpenAlexW4241645611MaRDI QIDQ3032373

László Fuchs, Saharon Shelah

Publication date: 1989

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2046728

zbMATH Keywords

valuation domainZFCKaplansky's problemdiamond principlenon-standard uniserial divisible modules

Mathematics Subject Classification ID

Applications of logic to commutative algebra (13L05) Nonstandard models of arithmetic (03H15) Divisibility and factorizations in commutative rings (13A05) Arithmetic rings and other special commutative rings (13F99)

Related Items (13)

Explicitly non-standard uniserial modules ⋮ A construction of nonstandard uniserial modules over valuation domains ⋮ Moduli uniseriali non standard ⋮ Interpreting modules in modules ⋮ László Fuchs' 70th birthday ⋮ On a Conjecture Regarding Nonstandard Uniserial Modules ⋮ A UNIFIED APPROACH TO VARIOUS GENERALIZATIONS OF ARMENDARIZ RINGS ⋮ A Transfer Theorem for Nonstandard Uniserials ⋮ Picard groups of some module categories ⋮ Definable additive categories: purity and model theory ⋮ Equimorphism classes of uniserial modules over valuation domains ⋮ On a non-vanishing Ext ⋮ Model theory of modules over a serial ring

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