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On Lie ideals with derivations as homomorphisms and anti-homomorphisms.
- Source :
-
Acta Mathematica Hungarica . 2003, Vol. 101 Issue 1/2, p79-82. 4p. - Publication Year :
- 2003
-
Abstract
- In [2, Theorem 3], Bell and Kappe proved that if d is a derivation of a prime ring R which acts as a homomorphism or an anti-homomorphism on a nonzero right ideal I of R, then d = 0 on R. In the present paper our objective is to extend this result to Lie ideals. The following result is proved: Let R be a 2-torsion free prime ring and U a nonzero Lie ideal of R such that u2 ε U, for all u ε U. If d is a derivation of R which acts as a homomorphism or an anti-homomorphism on U, then either d=0 or U ⫅ Z(R). [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02365294
- Volume :
- 101
- Issue :
- 1/2
- Database :
- Academic Search Index
- Journal :
- Acta Mathematica Hungarica
- Publication Type :
- Academic Journal
- Accession number :
- 14769027
- Full Text :
- https://doi.org/10.1023/B:AMHU.0000003893.61349.98