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

A result by Kulikov that does not extend to modules over general valuation domains


Authors: L. Salce and P. Zanardo
Journal: Proc. Amer. Math. Soc. 111 (1991), 643-649
MSC: Primary 13C05; Secondary 13A18, 13C12, 20K10
MathSciNet review: 1043419
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Abstract: Let $ R$ be a valuation domain. It is proved that every nonzero $ R$-module contains a nonzero pure uniserial submodule if and only if $ R$ is rank-one discrete.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1043419-5
PII: S 0002-9939(1991)1043419-5
Keywords: Valuation domains, uniserial modules, pure submodules
Article copyright: © Copyright 1991 American Mathematical Society