| Title:
|
Derivations with power central values on Lie ideals in prime rings (English) |
| Author:
|
Dhara, Basudeb |
| Author:
|
Sharma, R. K. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
58 |
| Issue:
|
1 |
| Year:
|
2008 |
| Pages:
|
147-153 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $R$ be a prime ring of char $R\ne 2$ with a nonzero derivation $d$ and let $U$ be its noncentral Lie ideal. If for some fixed integers $n_1\ge 0, n_2\ge 0, n_3\ge 0$, $( u^{n_1}[d(u),u]u^{n_2})^{n_3}\in Z(R)$ for all $u \in U$, then $R$ satisfies $S_4$, the standard identity in four variables. (English) |
| Keyword:
|
prime ring |
| Keyword:
|
derivation |
| Keyword:
|
extended centroid |
| Keyword:
|
martindale quotient ring |
| MSC:
|
16N60 |
| MSC:
|
16R50 |
| MSC:
|
16W10 |
| MSC:
|
16W25 |
| idZBL:
|
Zbl 1165.16303 |
| idMR:
|
MR2402531 |
| . |
| Date available:
|
2009-09-24T11:54:08Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128251 |
| . |
| Reference:
|
[1] J. Bergen, I. N. Herstein and J. W. Keer: Lie ideals and derivations of prime rings.J. Algebra 71 (1981), 259–267. MR 0627439, 10.1016/0021-8693(81)90120-4 |
| Reference:
|
[2] L. Carini and V. D. Filippis: Commutators with power central values on a Lie ideal.Pacific J. Math. 193 (2000), 269–278. MR 1755818, 10.2140/pjm.2000.193.269 |
| Reference:
|
[3] C. L. Chuang: GPI’s having coefficients in Utumi quotient rings.Proc. Amer. Math. Soc. 103 (1988), 723–728. MR 0947646, 10.1090/S0002-9939-1988-0947646-4 |
| Reference:
|
[4] T. S. Erickson, W. S. Martindale III and J. M. Osborn: Prime nonassociative algebras.Pacific J. Math. 60 (1975), 49–63. MR 0382379, 10.2140/pjm.1975.60.49 |
| Reference:
|
[5] N. Jacobson: PI-algebras, an Introduction.Lecture notes in Math., 441, Springer Verlag, New York, 1975. Zbl 0326.16013, MR 0369421 |
| Reference:
|
[6] N. Jacobson: Structure of Rings.Amer. Math. Soc. Colloq. Pub., 37, Amer. Math. Soc., Providence, RI, 1964. MR 0222106 |
| Reference:
|
[7] V. K. Kharchenko: Differential identity of prime rings.Algebra and Logic. 17 (1978), 155–168. MR 0541758, 10.1007/BF01670115 |
| Reference:
|
[8] C. Lanski: An engel condition with derivation.Proc. Amer. Math. Soc. 118 (1993), 731–734. Zbl 0821.16037, MR 1132851, 10.1090/S0002-9939-1993-1132851-9 |
| Reference:
|
[9] C. Lanski: Differential identities, Lie ideals, and Posner’s theorems.Pacific J. Math. 134 (1988), 275–297. Zbl 0614.16028, MR 0961236, 10.2140/pjm.1988.134.275 |
| Reference:
|
[10] W. S. Martindale III: Prime rings satisfying a generalized polynomial identity.J. Algebra 12 (1969), 576–584. MR 0238897, 10.1016/0021-8693(69)90029-5 |
| Reference:
|
[11] E. C. Posner: Derivation in prime rings.Proc. Amer. Math. Soc. 8 (1957), 1093–1100. MR 0095863, 10.1090/S0002-9939-1957-0095863-0 |
| . |
