ℵn-FREE MODULES OVER COMPLETE DISCRETE VALUATION DOMAINS WITH ALMOST TRIVIAL DUAL
2013 ◽
Vol 55
(2)
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pp. 369-380
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AbstractA 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.
2003 ◽
Vol 68
(3)
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pp. 439-447
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Keyword(s):
Keyword(s):
2006 ◽
Vol 56
(2)
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pp. 349-357
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2006 ◽
Vol 295
(1)
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pp. 269-288
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2019 ◽
Vol 27
(3)
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pp. 83-95
Keyword(s):
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