Geodesic
Splitting off free summands of torsion-free modules over complete DVRs
Glasgow mathematical journal, Tome 44 (2002) no. 2, pp. 349-351

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DOI

If R is a complete discrete valuation ring and M is a reduced, torsion-free R-module of rank \kappa, where \aleph_0 \leq \kappa < 2^ (\aleph_0), we show that M \prop\oplus_(\aleph_0) R \oplus C for some R-module C. As a consequence, it must be the case that M \prop M \oplus (\oplus{_\alpha}R), where \alpha \leq \aleph_0, and {\rm (End)_R}M/\rm (Fin)M has rank at least 2^ (\aleph_0), where Fin M denotes the set of endomorphisms of M with finite rank image. 
Göbel, Rüdiger; Paras, Agnes T. Splitting off free summands of torsion-free modules over complete DVRs. Glasgow mathematical journal, Tome 44 (2002) no. 2, pp. 349-351. doi: 10.1017/S0017089502020177
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     title = {Splitting off free summands of torsion-free modules over complete {DVRs}},
     journal = {Glasgow mathematical journal},
     pages = {349--351},
     year = {2002},
     volume = {44},
     number = {2},
     doi = {10.1017/S0017089502020177},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089502020177/}
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