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n-FREE MODULES OVER COMPLETE DISCRETE VALUATION DOMAINS WITH ALMOST TRIVIAL DUAL*

Published online by Cambridge University Press:  25 February 2013

RÜDIGER GÖBEL
Affiliation:
Fakultät für Mathematik, Universität Duisburg-Essen Campus Essen, 45117 Essen, Germany e-mail: ruediger.goebel@uni-due.de
SAHARON SHELAH
Affiliation:
The Hebrew University, Givat Ram, Jerusalem 91904, Israel, and Rutgers University, New Brunswick, NJ 08901, USA e-mail: Shelah@math.huji.ac.il
LUTZ STRÜNGMANN
Affiliation:
Fakultät für Informatik, Hochschule Mannheim 68163 Mannheim, Germany e-mail: l.struengmann@hs-mannheim.de
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Abstract

A module M over a commutative ring R has an almost trivial dual if there is no homomorphism from M onto a free R-module of countable infinite rank. Using a new combinatorial principle (the ℵn-Black Box), which is provable in ordinary set theory, we show that for every natural number n, there exist arbitrarily large ℵn-free R-modules with almost trivial duals, when R is a complete discrete valuation domain. A corresponding result for torsion modules is also obtained.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2013

Footnotes

*

Publication (GbShSm:981) in the second author's list of publications.

References

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n-FREE MODULES OVER COMPLETE DISCRETE VALUATION DOMAINS WITH ALMOST TRIVIAL DUAL*
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