An equation related to two-sided centralizers in prime ringsFošner, Maja (Avtor) Vukman, Joso (Avtor) matematikaalgebraprakolobarpolprakolobarfunkcijska identitetadvostranski centralizatormathematicsalgebraprime ringsemiprime ringfunctional identitytwo-sided centralizerWe prove the following result: Let ▫$R$▫ be a prime ring and let ▫$T : R to R$▫ be an additive mapping satisfying the relation ▫$nT(x^n) = T(x)x^{n-1} + xT(x)x^{n-2} + ... + x^{n-1}T(x)$▫ for all ▫$x in R$▫ where ▫$n > 1$▫ is some fixed integer. If ▫$char(R) = 0$▫ or ▫$n le char(R) ne 2$▫, then ▫$T$▫ is of the form ▫$T(x) = lambda x$▫ for all ▫$x in R$▫ and some fixed element ▫$lambda in C$▫ where ▫$C$▫ is the extended centroid of ▫$R$▫.20092015-07-10 12:24:01Delo ni kategorizirano49684sl