Abstract
Let Λ be a complete discrete valuation ring and let A be a torsion free Λ-module. The well known Prüfer-Kaplansky theorem states (see [3, Theorem 12]) that if the module A is reduced and countably generated then it is free. The main goal of this note is a general theorem of the Prüfer-Kaplansky type without assuming the completeness of Λ and without any countability condition on the module A.
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References
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© 1983 Springer-Verlag Berlin Heidelberg
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Procházka, L. (1983). A Generalization of a Prufer-Kaplansky Theorem. In: Göbel, R., Lady, L., Mader, A. (eds) Abelian Group Theory. Lecture Notes in Mathematics, vol 1006. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21560-9_43
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DOI: https://doi.org/10.1007/978-3-662-21560-9_43
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