On regular endomorphism rings of topological Abelian groups

Horea Florian Abrudan

Czechoslovak Mathematical Journal (2011)

  • Volume: 61, Issue: 2, page 521-530
  • ISSN: 0011-4642

Abstract

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We extend a result of Rangaswamy about regularity of endomorphism rings of Abelian groups to arbitrary topological Abelian groups. Regularity of discrete quasi-injective modules over compact rings modulo radical is proved. A characterization of torsion LCA groups A for which End c ( A ) is regular is given.

How to cite

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Abrudan, Horea Florian. "On regular endomorphism rings of topological Abelian groups." Czechoslovak Mathematical Journal 61.2 (2011): 521-530. <http://eudml.org/doc/197124>.

@article{Abrudan2011,
abstract = {We extend a result of Rangaswamy about regularity of endomorphism rings of Abelian groups to arbitrary topological Abelian groups. Regularity of discrete quasi-injective modules over compact rings modulo radical is proved. A characterization of torsion LCA groups $A$ for which $\{\rm End\}_c(A)$ is regular is given.},
author = {Abrudan, Horea Florian},
journal = {Czechoslovak Mathematical Journal},
keywords = {$m$-regular ring; discrete module; quasi-injective module; linearly compact group; LCA group; local product; regular endomorphism rings; topological Abelian groups; discrete modules; quasi-injective modules; linearly compact groups; LCA groups; local products},
language = {eng},
number = {2},
pages = {521-530},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On regular endomorphism rings of topological Abelian groups},
url = {http://eudml.org/doc/197124},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Abrudan, Horea Florian
TI - On regular endomorphism rings of topological Abelian groups
JO - Czechoslovak Mathematical Journal
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 2
SP - 521
EP - 530
AB - We extend a result of Rangaswamy about regularity of endomorphism rings of Abelian groups to arbitrary topological Abelian groups. Regularity of discrete quasi-injective modules over compact rings modulo radical is proved. A characterization of torsion LCA groups $A$ for which ${\rm End}_c(A)$ is regular is given.
LA - eng
KW - $m$-regular ring; discrete module; quasi-injective module; linearly compact group; LCA group; local product; regular endomorphism rings; topological Abelian groups; discrete modules; quasi-injective modules; linearly compact groups; LCA groups; local products
UR - http://eudml.org/doc/197124
ER -

References

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  2. Bourbaki, N., Obshchaya topologia. Topologicheskie gruppy. Chisla i svyazannye s nimi gruppy i prostranstva, Izdatel'stvo ``Nauka'', Moscow, 1969 (In Russian). French original: Elements de Mathematique. Topologie Generale. Ch. III--VIII, Hermann. MR0256328
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  8. Rangaswamy, K. M., 10.1016/0021-8693(67)90082-8, J. of Algebra 6 (1969), 271-280. (1969) MR0217180DOI10.1016/0021-8693(67)90082-8
  9. Stroppel, M., Locally Compact Groups, EMS Textbooks in Mathematics, European Mathematical Society Publishing House, Zurich (2006). (2006) Zbl1102.22005MR2226087
  10. Ursul, M., Topological Rings Satisfying Compactness Conditions, Mathematics and its Applications, Vol. 549, Kluwer Academic Publishers, Dordrecht-Boston-London (2002). (2002) Zbl1041.16037MR1959470
  11. Utumi, Y., On quotient rings, Osaka Math. J. 8 (1956), 1-18. (1956) Zbl0070.26601MR0078966
  12. Utumi, Y., 10.1016/0021-8693(67)90013-0, J. Algebra 6 (1967), 56-64. (1967) Zbl0161.03803MR0209321DOI10.1016/0021-8693(67)90013-0
  13. Warner, S., Topological Rings, North-Holland, Amsterdam-London-New York-Tokyo (1993). (1993) Zbl0785.13008MR1240057

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