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Abstract: The purpose of this paper is to prove the following result. Let ▫$m ge 1$▫, ▫$n ge 1$▫ be some fixed integers and let ▫$R$▫ be a prime ring with ▫$text{char}(R)= 0$▫ or ▫$(m+n)^2 < text{char}(R)$▫. Suppose there exists an additive mapping ▫$T colon R to R$▫ satisfying the relation ▫$2(m+n)^2T(x^3) = m(2m+n)T(x)x^2 + 2mnxT(x)x + n(2n+m)x^2T(x)$▫ for all ▫$x in R$▫. In this case ▫$T$▫ is a two-sided centralizer.
Keywords: matematika, algebra, kolobar, prakolobar, polprakolobar, Banachov prostor, Hilbertov prostor, algebra vseh omejenih linearnih operatorjev, standardna operatorska algebra, odvajanje, jordansko odvajanje, centralizator, algebra, ring, prime ring, semiprime ring, Banach space, Hilbert space, algebra of all bounded linear operators, standard operator algebra, derivation, Jordan derivation, left (right) centralizer, two-sided centralizer, left (right) Jordan centralizer, (m, n)-Jordan centralizer
Published in DKUM: 10.07.2015; Views: 1422; Downloads: 140
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