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

Salce, L.; Zanardo, P.

doi:10.1090/S0002-9939-1991-1043419-5

A result by Kulikov that does not extend to modules over general valuation domains
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by L. Salce and P. Zanardo PDF

Proc. Amer. Math. Soc. 111 (1991), 643-649 Request permission

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.

References

L. Fuchs, On divisible modules over domains, Abelian groups and modules (Udine, 1984) CISM Courses and Lect., vol. 287, Springer, Vienna, 1984, pp. 341–356. MR 789830, DOI 10.1007/978-3-7091-2814-5_{2}5
L. Fuchs and L. Salce, Uniserial modules over valuation rings, J. Algebra 85 (1983), no. 1, 14–31. MR 723064, DOI 10.1016/0021-8693(83)90115-1
László Fuchs and Luigi Salce, Modules over valuation domains, Lecture Notes in Pure and Applied Mathematics, vol. 97, Marcel Dekker, Inc., New York, 1985. MR 786121
L. Fuchs and L. Salce, Polyserial modules over valuation domains, Rend. Sem. Mat. Univ. Padova 80 (1988), 243–264 (1989). MR 988124

On the theory of Abelian groups of arbitrary cardinality

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Paolo Zanardo, Valuation domains without pathological modules, J. Algebra 96 (1985), no. 1, 1–8. MR 808835, DOI 10.1016/0021-8693(85)90033-X