Identities with Engel conditions on derivations
✍ Scribed by M. Tamer Koşan; Tsiu-Kwen Lee; Yiqiang Zhou
- Publisher
- Springer Vienna
- Year
- 2010
- Tongue
- English
- Weight
- 195 KB
- Volume
- 165
- Category
- Article
- ISSN
- 0026-9255
No coin nor oath required. For personal study only.
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We solve affirmatively a problem, raised by Kharchenko, on identities with compositions of skew derivations: We define the notion of trivial identities with compositions of skew derivations, which is unique in a certain sense. It is proved that if a prime ring R satisfies a nontrivial identity with
An associative ring R without unity is called radical if it coincides with its Jacobson radical, which means that the set of all elements of R forms a group denoted by R ( under the circle operation r ( s s r q s q rs on R. It is proved that, for a radical ring R, the group R ( satisfies an n-Engel