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Nilpotency of Centralizers in Prime Rings | ||
| Iraqi Journal of Science | ||
| Article 1, Volume 56, Issue 1, 2015, Pages 214-217 | ||
| Authors | ||
| Abdulrahman H. Majeed; Faten Adel Shalal | ||
| Abstract | ||
| E. C. Posner proved that if λ and δ are derivations of a prime ring R with characteristic not equal 2 , then λδ=0 implies that either λ=0 or δ=0 . David W.Jensen extend this result by showing that , without any characteristic restriction , λδ^m=0 implies either λ=0 or δ^(4m-1)=0 , also he proved that λ^n δ=0 implies either δ^2=0 or λ^(12n-9)=0 , and finally , in general when λ^n δ^m=0 , he showed that if λ and δ are commute , then at least one of the derivations must be nilpotent .Here we ask the possibility if the same results of David can be satisfied on R with replacing the derivations λ andδ with centralizers T and G. | ||
| Keywords | ||
| semiprime ring; prime ring; derivation; left; centralizer; Jordan centralizer; nilpotent centralizer | ||
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