On the Jacobson radical of graded rings

Andrei V. Kelarev

Commentationes Mathematicae Universitatis Carolinae (1992)

  • Volume: 33, Issue: 1, page 21-24
  • ISSN: 0010-2628

Abstract

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All commutative semigroups S are described such that the Jacobson radical is homogeneous in each ring graded by S .

How to cite

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Kelarev, Andrei V.. "On the Jacobson radical of graded rings." Commentationes Mathematicae Universitatis Carolinae 33.1 (1992): 21-24. <http://eudml.org/doc/21827>.

@article{Kelarev1992,
abstract = {All commutative semigroups $S$ are described such that the Jacobson radical is homogeneous in each ring graded by $S$.},
author = {Kelarev, Andrei V.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Jacobson radical; $G$-graded ring ($G$ a commutative semigroup); Jacobson radical; strongly -graded ring; locally nilpotent Jacobson radical; unique product group; -nilpotency},
language = {eng},
number = {1},
pages = {21-24},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On the Jacobson radical of graded rings},
url = {http://eudml.org/doc/21827},
volume = {33},
year = {1992},
}

TY - JOUR
AU - Kelarev, Andrei V.
TI - On the Jacobson radical of graded rings
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1992
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 33
IS - 1
SP - 21
EP - 24
AB - All commutative semigroups $S$ are described such that the Jacobson radical is homogeneous in each ring graded by $S$.
LA - eng
KW - Jacobson radical; $G$-graded ring ($G$ a commutative semigroup); Jacobson radical; strongly -graded ring; locally nilpotent Jacobson radical; unique product group; -nilpotency
UR - http://eudml.org/doc/21827
ER -

References

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  1. Bergman G.M., On Jacobson radicals of graded rings, preprint. 
  2. Clifford A.H., Preston G.B., The Algebraic Theory of Semigroups, Vol. 1., Math. Surveys of the Amer. Math. Soc. 7 (1961). Zbl0238.20076MR0132791
  3. Cohen M., Montgomery S., Group graded rings, smash products and group actions, Trans. Amer. Math. Soc. 282 (1984), 237-258. Addendum: Trans. Amer. Math. Soc. 300 (1987), 810-811. (1984) Zbl0533.16001MR0728711
  4. Cohen M., Rowen L.H., Group graded rings, Commun. Algebra 11 (1983), 1253-1270. (1983) Zbl0522.16001MR0696990
  5. Jespers E., On radicals of graded rings, Commun. Algebra 13 (1985), 2457-2472. (1985) Zbl0575.16001MR0807485
  6. Jespers E., When is the Jacobson radical of a semigroup ring of a commutative semigroup homogeneous?, Commun. Algebra 109 (1987), 549-560. (1987) Zbl0619.20045MR0902968
  7. Jespers E., Krempa J., Puczylowski E.R., On radicals of graded rings, Commun. Algebra 10 (1982), 1849-1854. (1982) Zbl0493.16003MR0674695
  8. Jespers E., Puczylowski E.R., The Jacobson and Brown-McCoy radicals of rings graded by free groups, Commun. Algebra 19 (1991), 551-558. (1991) Zbl0721.16023MR1100363
  9. Jespers E., Wauters P., A description of the Jacobson radical of semigroups rings of commutative semigroup, Group and Semigroup Rings, Johannesburg, 1986, 43-89. Zbl0599.20103MR0860052
  10. Kelarev A.V., When is the radical of a band sum of rings homogeneous?, Commun. Algebra 18 (1990), 585-603. (1990) Zbl0697.20049MR1047329
  11. Munn W.D., On commutative semigroup algebras, Math. Proc. Camb. Phil. Soc. 93 (1983), 237-246. (1983) Zbl0528.20053MR0691992
  12. Okninski J., On the radical of semigroup algebras satisfying polynomial identities, Math. Proc. Camb. Phil. Soc. 99 (1986), 45-50. (1986) Zbl0583.20052MR0809496
  13. Okninski J., Wauters P., Radicals of semigroup rings of commutative semigroups, Math. Proc. Camb. Phil. Soc. 99 (1986), 435-445. (1986) Zbl0599.20104MR0830356
  14. Puczylowski E.R., Behaviour of radical properties of rings under some algebraic constructions, Coll. Math. Soc. János Bolyai 38 (1982), 449-480. (1982) Zbl0607.16006MR0899123
  15. Teply M.L., Turman E.G., Quesada A., On semisimple semigroup rings, Proc. Amer. Math. Soc. 79 (1980), 157-163. (1980) Zbl0445.20043MR0565329

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