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Splitting off free summands of torsion-free modules over complete DVRs

Published online by Cambridge University Press:  25 July 2002

Rüdiger Göbel  and
Agnes T. Paras
Rüdiger Göbel
Affiliation:
Fachbereich 6, Mathematik und Informatik, Universität Essen, 45117 Essen, Germany e-mail: r.goebel@uni-essen.de
Agnes T. Paras
Affiliation:
Department of Mathematics, University of the Philippines at Diliman 1101 Quezon City, Philippines e-mail: agnes@math01.cs.upd.edu.ph
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Abstract

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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.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 44 , Issue 2 , May 2002 , pp. 349 - 351
Copyright
2002 Glasgow Mathematical Journal Trust

Footnotes

This work is supported by Project No. G-545-173.06/97 of the German-Israeli Foundation for Scientific Research & Development.