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

Title & Authors
A RESULT ON GENERALIZED DERIVATIONS WITH ENGEL CONDITIONS ON ONE-SIDED IDEALS
Demir, Cagri; Argac, Nurcan;

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 $\small{[g(x^m)x^n,\;x^r]_k\;=\;0}$ for all x $\small{\in}$ I, then there exists a $\small{\in}$ U such that g(x) = xa for all x $\small{\in}$ R except when $\small{R\;{\cong}\;=M_2}$(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;
Language
English
Cited by
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2.
A Characterization of Generalized Derivations on Prime Rings, Communications in Algebra, 2016, 44, 8, 3201
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