Products of small modules

Peter Kálnai; Jan Žemlička

Commentationes Mathematicae Universitatis Carolinae (2014)

  • Volume: 55, Issue: 1, page 9-16
  • ISSN: 0010-2628

Abstract

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Module is said to be small if it is not a union of strictly increasing infinite countable chain of submodules. We show that the class of all small modules over self-injective purely infinite ring is closed under direct products whenever there exists no strongly inaccessible cardinal.

How to cite

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Kálnai, Peter, and Žemlička, Jan. "Products of small modules." Commentationes Mathematicae Universitatis Carolinae 55.1 (2014): 9-16. <http://eudml.org/doc/260781>.

@article{Kálnai2014,
abstract = {Module is said to be small if it is not a union of strictly increasing infinite countable chain of submodules. We show that the class of all small modules over self-injective purely infinite ring is closed under direct products whenever there exists no strongly inaccessible cardinal.},
author = {Kálnai, Peter, Žemlička, Jan},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {small module; self-injectivity; von Neumann regular ring; purely infinite rings; direct sums; direct products; strongly inaccessible cardinals; small modules; self-injectivity; purely infinite rings; direct sums; direct products; strongly inaccessible cardinals; von Neumann regular rings},
language = {eng},
number = {1},
pages = {9-16},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Products of small modules},
url = {http://eudml.org/doc/260781},
volume = {55},
year = {2014},
}

TY - JOUR
AU - Kálnai, Peter
AU - Žemlička, Jan
TI - Products of small modules
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2014
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 55
IS - 1
SP - 9
EP - 16
AB - Module is said to be small if it is not a union of strictly increasing infinite countable chain of submodules. We show that the class of all small modules over self-injective purely infinite ring is closed under direct products whenever there exists no strongly inaccessible cardinal.
LA - eng
KW - small module; self-injectivity; von Neumann regular ring; purely infinite rings; direct sums; direct products; strongly inaccessible cardinals; small modules; self-injectivity; purely infinite rings; direct sums; direct products; strongly inaccessible cardinals; von Neumann regular rings
UR - http://eudml.org/doc/260781
ER -

References

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  9. Trlifaj J., Steady rings may contain large sets of orthogonal idempotents, Proc. Conf. Abelian Groups and Modules (Padova 1994), Kluwer, Dordrecht, 1995, pp. 467–473. Zbl0845.16009MR1378220
  10. Zelenyuk E.G., Ultrafilters and topologies on groups, de Gruyter Expositions in Mathematics, 50, de Gruyter, Berlin, 2011. Zbl1215.22001MR2768144
  11. Žemlička J., 10.1090/conm/273/04444, Contemporary Mathematics 273 (2001), 301–308. Zbl0988.16003MR1817172DOI10.1090/conm/273/04444
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