Notes on slender prime rings

Robert El Bashir; Tomáš Kepka

Commentationes Mathematicae Universitatis Carolinae (1996)

  • Volume: 37, Issue: 2, page 419-422
  • ISSN: 0010-2628

Abstract

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If R is a prime ring such that R is not completely reducible and the additive group R ( + ) is not complete, then R is slender.

How to cite

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El Bashir, Robert, and Kepka, Tomáš. "Notes on slender prime rings." Commentationes Mathematicae Universitatis Carolinae 37.2 (1996): 419-422. <http://eudml.org/doc/247912>.

@article{ElBashir1996,
abstract = {If $R$ is a prime ring such that $R$ is not completely reducible and the additive group $R(+)$ is not complete, then $R$ is slender.},
author = {El Bashir, Robert, Kepka, Tomáš},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {ring; prime; slender; slender rings; prime rings; linear topologies; metrizable filtrations; additive groups; cyclic modules},
language = {eng},
number = {2},
pages = {419-422},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Notes on slender prime rings},
url = {http://eudml.org/doc/247912},
volume = {37},
year = {1996},
}

TY - JOUR
AU - El Bashir, Robert
AU - Kepka, Tomáš
TI - Notes on slender prime rings
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1996
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 37
IS - 2
SP - 419
EP - 422
AB - If $R$ is a prime ring such that $R$ is not completely reducible and the additive group $R(+)$ is not complete, then $R$ is slender.
LA - eng
KW - ring; prime; slender; slender rings; prime rings; linear topologies; metrizable filtrations; additive groups; cyclic modules
UR - http://eudml.org/doc/247912
ER -

References

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  1. Anderson F.W., Fuller K.R., Rings and Categories of Modules, 2 n d edition, Springer New York (1992). (1992) Zbl0765.16001MR1245487
  2. El Bashir R., Kepka T., On when small semiprime rings are slender, to appear. Zbl0854.16015
  3. Dimitrić R., Slender modules over domains, Commun. in Algebra 11 (1983), 1685-1700. (1983) MR0702414
  4. Eklof P., Mekler A., Almost Free Modules, North-Holland New York (1990). (1990) Zbl0718.20027MR1055083
  5. Heinlein G., Vollreflexive Ringe und schlanke Moduln, Dissertation Erlangen (1971). (1971) 
  6. Nunkee R., Slender groups, Acta Sci. Math. Szeged 23 (1962), 67-73. (1962) MR0144968

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