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http://dx.doi.org/10.4134/JKMS.2010.47.3.483

A RESULT ON GENERALIZED DERIVATIONS WITH ENGEL CONDITIONS ON ONE-SIDED IDEALS  

Demir, Cagri (DEPARTMENT OF MATHEMATICS SCIENCE FACULTY EGE UNIVERSITY)
Argac, Nurcan (DEPARTMENT OF MATHEMATICS SCIENCE FACULTY EGE UNIVERSITY)
Publication Information
Journal of the Korean Mathematical Society / v.47, no.3, 2010 , pp. 483-494 More about this Journal
Abstract
Let R be a non-commutative prime ring and I a non-zero left ideal of R. Let U be the left Utumi quotient ring of R and C be the center of U and k, m, n, r fixed positive integers. If there exists a generalized derivation g of R such that $[g(x^m)x^n,\;x^r]_k\;=\;0$ for all x $\in$ I, then there exists a $\in$ U such that g(x) = xa for all x $\in$ R except when $R\;{\cong}\;=M_2$(GF(2)) and I[I, I] = 0.
Keywords
prime rings; derivations; generalized derivations; left Utumi quotient rings; two-sided Martindale quotient ring; differential identities; Engel condition;
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