Generalized derivations of left faithful rings
1999; Taylor & Francis; Volume: 27; Issue: 8 Linguagem: Inglês
10.1080/00927879908826682
ISSN1532-4125
Autores Tópico(s)Rings, Modules, and Algebras
ResumoAbstract Let R be a left faithful ringU its right Utumi quotient ring and ρ a dense right ideal of R. An additive map g: ρ → U is called a generalized derivation if there exists a derivation δ of ρ into U such that for all x,y∈ρ. In this note, we prove that there exists an element a∈ U such that for all x ∈ ρ. From this characterization, it is proved that if R is a semiprime ring and if g is a generalized derivation with nilpotent values of bounded index, then g = 0. Analogous results are also obtained for the case of generalized derivations with nilpotent values on Lie ideals or one-sided ideals.
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