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

top
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

top

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

top
  1. Abrudan, H. F., Ursul, M., Boundedness of topological endomorphism rings of torsion Abelian groups, Contr. to Gen. Algebra 17 (2006), 1-8. (2006) Zbl1119.20049MR2237800
  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
  3. Faith, C., Algebra II---Ring Theory, Springer-Verlag, Berlin-Heidelberg-New York (1976). (1976) MR0427349
  4. Faith, C., Utumi, Y., 10.1007/BF01589182, Arch. Math. 15 (1964), 166-174. (1964) Zbl0131.27502MR0166226DOI10.1007/BF01589182
  5. Fuchs, L., Infinite Abelian Groups, Vol. II, Academic Press, New York (1973). (1973) Zbl0257.20035MR0349869
  6. Johnson, R. E., Wong, E. T., 10.1112/jlms/s1-36.1.260, J. Lond. Math. Soc. 36 (1961), 260-268. (1961) Zbl0103.02203MR0131445DOI10.1112/jlms/s1-36.1.260
  7. Osofsky, B. L., 10.4153/CJM-1968-086-3, Canad. J. Math. 20 (1968), 895-903. (1968) Zbl0162.05101MR0231856DOI10.4153/CJM-1968-086-3
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.