Generalized derivations with engel conditions on one-sided ideals
Articles > Article · 2008
Authors: Einine Albas, Nurcan ARGAÇ, Vincenzo De Filippis
COMMUNICATIONS IN ALGEBRA, Journal Indexed in SCI Expanded, International, 2008, vol 36, pp 2063-2071
DOI: 10.1080/00927870801949328
Summary
Let R be a noncommutative prime ring and I a nonzero left ideal of R. Let g be a generalized derivation of R such that [g(r(k)), r(k)](n) = 0 for all r is an element of I, where k, n are fixed positive integers. Then there exists c is an element of U, the left Utumi quotient ring of R, such that g(x) = xc and I(c-alpha) = 0 for a suitable alpha is an element of C. In particular we have that g(x) = alpha x, for all x is an element of I.