A RESULT ON GENERALIZED DERIVATIONS WITH ENGEL CONDITIONS ON ONE-SIDED IDEALS
Articles > Article ยท 2010
Authors: Cagri Demir, Nurcan Argac
Journal of the Korean Mathematical Society, International, WoS, 2010, vol 47, pp 483-494
DOI: 10.4134/jkms.2010.47.3.483
Summary
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.