Generalized Derivations with Engel Conditions on One-Sided Ideals
Makaleler > Tam Makale · 2008
Yazarlar: Emine ALBAŞ, Nurcan Argaç, Vincenzo De Filippis
Communications in Algebra, Uluslararası, Wos, 2008, cilt 36, ss 2063-2071
DOI: 10.1080/00927870801949328
Özet
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 ∈ I, where k, n are fixed positive integers. Then there exists c ∈ U, the left Utumi quotient ring of R, such that g(x) = xc and I(c − α) = 0 for a suitable α ∈ C. In particular we have that g(x) = α x, for all x ∈ I.