A note on semilocal group rings

Angelina Y. M. Chin

Czechoslovak Mathematical Journal (2002)

  • Volume: 52, Issue: 4, page 749-755
  • ISSN: 0011-4642

Abstract

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Let R be an associative ring with identity and let J ( R ) denote the Jacobson radical of R . R is said to be semilocal if R / J ( R ) is Artinian. In this paper we give necessary and sufficient conditions for the group ring R G , where G is an abelian group, to be semilocal.

How to cite

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Chin, Angelina Y. M.. "A note on semilocal group rings." Czechoslovak Mathematical Journal 52.4 (2002): 749-755. <http://eudml.org/doc/30741>.

@article{Chin2002,
abstract = {Let $R$ be an associative ring with identity and let $J(R)$ denote the Jacobson radical of $R$. $R$ is said to be semilocal if $R/J(R)$ is Artinian. In this paper we give necessary and sufficient conditions for the group ring $RG$, where $G$ is an abelian group, to be semilocal.},
author = {Chin, Angelina Y. M.},
journal = {Czechoslovak Mathematical Journal},
keywords = {semilocal; group ring; semilocal rings; group rings},
language = {eng},
number = {4},
pages = {749-755},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A note on semilocal group rings},
url = {http://eudml.org/doc/30741},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Chin, Angelina Y. M.
TI - A note on semilocal group rings
JO - Czechoslovak Mathematical Journal
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 52
IS - 4
SP - 749
EP - 755
AB - Let $R$ be an associative ring with identity and let $J(R)$ denote the Jacobson radical of $R$. $R$ is said to be semilocal if $R/J(R)$ is Artinian. In this paper we give necessary and sufficient conditions for the group ring $RG$, where $G$ is an abelian group, to be semilocal.
LA - eng
KW - semilocal; group ring; semilocal rings; group rings
UR - http://eudml.org/doc/30741
ER -

References

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  2. 10.4153/CJM-1963-067-0, Canad. J.  Math. 15 (1963), 650–685. (1963) Zbl0121.03502MR0153705DOI10.4153/CJM-1963-067-0
  3. 10.4153/CJM-1973-098-1, Canad. J.  Math. 25 (1973), 922–928. (1973) Zbl0269.16012MR0338054DOI10.4153/CJM-1973-098-1
  4. An elementary note on group rings, J.  Reine Angew. Math. 242 (1970), 148–162. (1970) MR0274609
  5. Lectures on Rings and Modules, Blaisdell, Waltham, Mass., 1966. (1966) Zbl0143.26403MR0206032
  6. Semilocal group rings and tensor products, Michigan Math.  J. 22 (1975), 309–313. (1975) MR0393107
  7. 10.1007/BF02756627, Israel J.  Math. 19 (1974), 67–107. (1974) MR0357477DOI10.1007/BF02756627
  8. Sur les anneaux de groupes, C.  R.  Acad. Sci. Paris Ser.  A 273 (1971), 84–87. (1971) Zbl0275.16013MR0288189
  9. Some results on semi-perfect group rings, Canad. J.  Math. 28 (1974), 121–129. (1974) Zbl0242.16007MR0330212

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