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SOME RESULTS ( | ||
| Iraqi Journal of Science | ||
| Article 1, Volume 49, Issue 1, 2008, Pages 188-191 | ||
| Authors | ||
| Kassim Abdul-Hameed; Abdul-Ruhman Hameed | ||
| Abstract | ||
| Let R be a prime ring and d: R ~R be a (c.rj-derivation of R. V be a left ideal of R which is semiprime as a ring .In this paper we proved that if d is a nonzero endomorphism on R .and d(R)cZ(R),then R is commutative .and we show by an example the condition d is an endomorphism on R can not be excluded. Also, we proved the following. )i) If Ua⊂Z(R) (or aU⊂Z(R)), for aϵR), then a=0 or R is commutative. (ii) If d is a nonzero on R such that d(U)a⊂Z(R) (or ad(U)⊂Z(R) for aϵZ(R), then either a=0 or | ||
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