| Title:
|
$(\sigma,\tau)$-derivations on prime near rings (English) |
| Author:
|
Ashraf, Mohammad |
| Author:
|
Ali, Asma |
| Author:
|
Ali, Shakir |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
40 |
| Issue:
|
3 |
| Year:
|
2004 |
| Pages:
|
281-286 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
There is an increasing body of evidence that prime near-rings with derivations have ring like behavior, indeed, there are several results (see for example [1], [2], [3], [4], [5] and [8]) asserting that the existence of a suitably-constrained derivation on a prime near-ring forces the near-ring to be a ring. It is our purpose to explore further this ring like behaviour. In this paper we generalize some of the results due to Bell and Mason [4] on near-rings admitting a special type of derivation namely $(\sigma ,\tau )$- derivation where $\sigma ,\tau $ are automorphisms of the near-ring. Finally, it is shown that under appropriate additional hypothesis a near-ring must be a commutative ring. (English) |
| Keyword:
|
prime near-ring |
| Keyword:
|
derivation |
| Keyword:
|
$\sigma $-derivation |
| Keyword:
|
$(\sigma, \tau )$-derivation |
| Keyword:
|
$(\sigma, \tau )$-commuting derivation |
| MSC:
|
16U70 |
| MSC:
|
16W25 |
| MSC:
|
16Y30 |
| idZBL:
|
Zbl 1114.16040 |
| idMR:
|
MR2107023 |
| . |
| Date available:
|
2008-06-06T22:43:56Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107910 |
| . |
| Reference:
|
[1] Beidar K. I., Fong Y., Wang X. K.: Posner and Herstein theorems for derivations of 3-prime near-rings.Comm. Algebra 24 (5) (1996), 1581–1589. Zbl 0849.16039, MR 1386483 |
| Reference:
|
[2] Bell H. E.: On derivations in near-rings, II.Kluwer Academic Publishers Netherlands (1997), 191–197. Zbl 0911.16026, MR 1492193 |
| Reference:
|
[3] Bell H. E., Mason G.: On derivations in near-rings and rings.Math. J. Okayama Univ. 34 (1992), 135–144. Zbl 0810.16042, MR 1272613 |
| Reference:
|
[4] Bell H. E., Mason G.: On derivations in near-rings.Near-Rings and Near-Fields (G. Betsch, ed.) North-Holland, Amsterdam (1987), 31–35. Zbl 0619.16024, MR 0890753 |
| Reference:
|
[5] Kamal Ahmad A. M.: $\sigma $- derivations on prime near-rings.Tamkang J. Math. 32 2 (2001), 89–93. MR 1826415 |
| Reference:
|
[6] Meldrum J. D. P.: Near-rings and Their Link with Groups.Pitman, 1985. MR 0854275 |
| Reference:
|
[7] Posner E. C.: Derivations in prime rings.Proc. Amer. Math. Soc. 8 (1957), 1093–1100. MR 0095863 |
| Reference:
|
[8] Wang X. K.: Derivations in prime near-rings.Proc. Amer. Math. Soc. 121 (1994), 361–366. Zbl 0811.16040, MR 1181177 |
| . |
