Separable ℵ k -free modules with almost trivial dual

Daniel Herden; Héctor Gabriel Salazar Pedroza

Commentationes Mathematicae Universitatis Carolinae (2016)

  • Volume: 57, Issue: 1, page 7-20
  • ISSN: 0010-2628

Abstract

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An R -module M has an almost trivial dual if there are no epimorphisms from M to the free R -module of countable infinite rank R ( ω ) . For every natural number k > 1 , we construct arbitrarily large separable ℵ k -free R -modules with almost trivial dual by means of Shelah’s Easy Black Box, which is a combinatorial principle provable in ZFC.

How to cite

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Herden, Daniel, and Pedroza, Héctor Gabriel Salazar. "Separable $\aleph _k$-free modules with almost trivial dual." Commentationes Mathematicae Universitatis Carolinae 57.1 (2016): 7-20. <http://eudml.org/doc/276790>.

@article{Herden2016,
abstract = {An $R$-module $M$ has an almost trivial dual if there are no epimorphisms from $M$ to the free $R$-module of countable infinite rank $R^\{(\omega )\}$. For every natural number $k>1$, we construct arbitrarily large separable $\aleph _k$-free $R$-modules with almost trivial dual by means of Shelah’s Easy Black Box, which is a combinatorial principle provable in ZFC.},
author = {Herden, Daniel, Pedroza, Héctor Gabriel Salazar},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {prediction principles; almost free modules; dual modules},
language = {eng},
number = {1},
pages = {7-20},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Separable $\aleph _k$-free modules with almost trivial dual},
url = {http://eudml.org/doc/276790},
volume = {57},
year = {2016},
}

TY - JOUR
AU - Herden, Daniel
AU - Pedroza, Héctor Gabriel Salazar
TI - Separable $\aleph _k$-free modules with almost trivial dual
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2016
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 57
IS - 1
SP - 7
EP - 20
AB - An $R$-module $M$ has an almost trivial dual if there are no epimorphisms from $M$ to the free $R$-module of countable infinite rank $R^{(\omega )}$. For every natural number $k>1$, we construct arbitrarily large separable $\aleph _k$-free $R$-modules with almost trivial dual by means of Shelah’s Easy Black Box, which is a combinatorial principle provable in ZFC.
LA - eng
KW - prediction principles; almost free modules; dual modules
UR - http://eudml.org/doc/276790
ER -

References

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  11. Herden D., Constructing ℵ k -free structures, Habilitationsschrift, University of Duisburg-Essen, 2013. 
  12. Hill P., 10.1090/S0002-9947-1974-0352294-8, Trans. Amer. Math. Soc. 196 (1974), 191–201. MR0352294DOI10.1090/S0002-9947-1974-0352294-8
  13. Jech T., Set Theory, Monographs in Mathematics, Springer, Berlin, 2002. Zbl1007.03002MR1940513
  14. Salazar Pedroza H.G., Combinatorial principles and ℵ k -free modules, PhD Thesis, University of Duisburg-Essen, 2012. 
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