On the Jacobson radical of strongly group graded rings

Andrei V. Kelarev

Commentationes Mathematicae Universitatis Carolinae (1994)

  • Volume: 35, Issue: 3, page 575-580
  • ISSN: 0010-2628

Abstract

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For any non-torsion group G with identity e , we construct a strongly G -graded ring R such that the Jacobson radical J ( R e ) is locally nilpotent, but J ( R ) is not locally nilpotent. This answers a question posed by Puczyłowski.

How to cite

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Kelarev, Andrei V.. "On the Jacobson radical of strongly group graded rings." Commentationes Mathematicae Universitatis Carolinae 35.3 (1994): 575-580. <http://eudml.org/doc/247627>.

@article{Kelarev1994,
abstract = {For any non-torsion group $G$ with identity $e$, we construct a strongly $G$-graded ring $R$ such that the Jacobson radical $J(R_e)$ is locally nilpotent, but $J(R)$ is not locally nilpotent. This answers a question posed by Puczyłowski.},
author = {Kelarev, Andrei V.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {strongly graded rings; radicals; local nilpotency; Jacobson radical; strongly -graded ring; locally nilpotent Jacobson radical; unique product group; -nilpotency},
language = {eng},
number = {3},
pages = {575-580},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On the Jacobson radical of strongly group graded rings},
url = {http://eudml.org/doc/247627},
volume = {35},
year = {1994},
}

TY - JOUR
AU - Kelarev, Andrei V.
TI - On the Jacobson radical of strongly group graded rings
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1994
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 35
IS - 3
SP - 575
EP - 580
AB - For any non-torsion group $G$ with identity $e$, we construct a strongly $G$-graded ring $R$ such that the Jacobson radical $J(R_e)$ is locally nilpotent, but $J(R)$ is not locally nilpotent. This answers a question posed by Puczyłowski.
LA - eng
KW - strongly graded rings; radicals; local nilpotency; Jacobson radical; strongly -graded ring; locally nilpotent Jacobson radical; unique product group; -nilpotency
UR - http://eudml.org/doc/247627
ER -

References

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