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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Direct sums of countably generated modules over complete discrete valuation rings


Author: Chang Mo Bang
Journal: Proc. Amer. Math. Soc. 28 (1971), 381-388
MSC: Primary 20.30; Secondary 13.00
DOI: https://doi.org/10.1090/S0002-9939-1971-0276326-3
MathSciNet review: 0276326
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0276326-3
Keywords: Direct sums of countably generated reduced modules, complete discrete valuation ring, Ulm invariant, basis type, height-preserving isomorphism, the Ulm theorem, the Kolettis theorem
Article copyright: © Copyright 1971 American Mathematical Society