Direct sums of countably generated modules over complete discrete valuation rings

Bang, Chang Mo

doi:10.1090/S0002-9939-1971-0276326-3

Direct sums of countably generated modules over complete discrete valuation rings
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Proc. Amer. Math. Soc. 28 (1971), 381-388 Request permission

Abstract:

Throughout this paper, $R$ will denote an arbitrary but fixed complete discrete valuation ring. We shall show that two reduced $R$-modules which are direct sums of countably generated $R$-modules are isomorphic if and only if they have the same Ulm invariants and the same basis type. This is a generalization of the celebrated Ulm and Kolettis theorem.

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