Some results concerning additive mappings and derivations on semiprime rings
Fošner, Ajda ; Vukman, Joso
Naj bo ▫$R$▫ polprakolobar in ▫$f \colon R \to R$▫ aditivna preslikava, ki zadošča ▫$[f(x),x^2] = 0$▫ za vse ▫$x \in R$▫. V članku je dokazano, da je potem ▫$[f(x),x] = 0$▫ za vse ▫$x \in R$▫. S ...pomočjo tega rezultata lahko dokažemo naslednje. Naj bo ▫$R$▫ polprakolobar in ▫$D,G \colon R \to R$▫ odvajanji. Predpostavimo, da je ▫$[D^2(x) + G(x),x^2] = 0$▫ za vse ▫$x \in R$▫. Potem ▫$D$▫ in ▫$G$▫ slikata ▫$R$▫ v njegov center.
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