| Title:
|
On the Jacobson radical of graded rings (English) |
| Author:
|
Kelarev, A. V. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
33 |
| Issue:
|
1 |
| Year:
|
1992 |
| Pages:
|
21-24 |
| . |
| Category:
|
math |
| . |
| Summary:
|
All commutative semigroups $S$ are described such that the Jacobson radical is homogeneous in each ring graded by $S$. (English) |
| Keyword:
|
Jacobson radical |
| Keyword:
|
$G$-graded ring ($G$ a commutative semigroup) |
| MSC:
|
16A20 |
| MSC:
|
16A21 |
| MSC:
|
16N20 |
| MSC:
|
16N40 |
| MSC:
|
16W50 |
| MSC:
|
20C05 |
| MSC:
|
20M14 |
| idZBL:
|
Zbl 0815.16025 |
| idMR:
|
MR1173741 |
| . |
| Date available:
|
2009-01-08T17:49:51Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118465 |
| . |
| Reference:
|
[1] Bergman G.M.: On Jacobson radicals of graded rings.preprint. |
| Reference:
|
[2] Clifford A.H., Preston G.B.: The Algebraic Theory of Semigroups.Vol. 1., Math. Surveys of the Amer. Math. Soc. 7 (1961). Zbl 0238.20076, MR 0132791 |
| Reference:
|
[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. Zbl 0533.16001, MR 0728711 |
| Reference:
|
[4] Cohen M., Rowen L.H.: Group graded rings.Commun. Algebra 11 (1983), 1253-1270. Zbl 0522.16001, MR 0696990 |
| Reference:
|
[5] Jespers E.: On radicals of graded rings.Commun. Algebra 13 (1985), 2457-2472. Zbl 0575.16001, MR 0807485 |
| Reference:
|
[6] Jespers E.: When is the Jacobson radical of a semigroup ring of a commutative semigroup homogeneous?.Commun. Algebra 109 (1987), 549-560. Zbl 0619.20045, MR 0902968 |
| Reference:
|
[7] Jespers E., Krempa J., Puczylowski E.R.: On radicals of graded rings.Commun. Algebra 10 (1982), 1849-1854. Zbl 0493.16003, MR 0674695 |
| Reference:
|
[8] Jespers E., Puczylowski E.R.: The Jacobson and Brown-McCoy radicals of rings graded by free groups.Commun. Algebra 19 (1991), 551-558. Zbl 0721.16023, MR 1100363 |
| Reference:
|
[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. MR 0860052 |
| Reference:
|
[10] Kelarev A.V.: When is the radical of a band sum of rings homogeneous?.Commun. Algebra 18 (1990), 585-603. Zbl 0697.20049, MR 1047329 |
| Reference:
|
[11] Munn W.D.: On commutative semigroup algebras.Math. Proc. Camb. Phil. Soc. 93 (1983), 237-246. Zbl 0528.20053, MR 0691992 |
| Reference:
|
[12] Okninski J.: On the radical of semigroup algebras satisfying polynomial identities.Math. Proc. Camb. Phil. Soc. 99 (1986), 45-50. Zbl 0583.20052, MR 0809496 |
| Reference:
|
[13] Okninski J., Wauters P.: Radicals of semigroup rings of commutative semigroups.Math. Proc. Camb. Phil. Soc. 99 (1986), 435-445. Zbl 0599.20104, MR 0830356 |
| Reference:
|
[14] Puczylowski E.R.: Behaviour of radical properties of rings under some algebraic constructions.Coll. Math. Soc. János Bolyai 38 (1982), 449-480. MR 0899123 |
| Reference:
|
[15] Teply M.L., Turman E.G., Quesada A.: On semisimple semigroup rings.Proc. Amer. Math. Soc. 79 (1980), 157-163. Zbl 0445.20043, MR 0565329 |
| . |
