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72. On generalized Jordan triple ([alpha], [beta]) [sup] [ast]-derivations and related mappingsShakir Ali, Ajda Fošner, Maja Fošner, Mohammad Salahuddin Khan, 2013, original scientific article Abstract: Let ▫$R$▫ be a 2-torsion free semiprime ▫$\ast$▫-ring and let ▫$\alpha, \beta$▫ be surjective endomorphisms of ▫$R$▫. The aim of the paper is to show that every generalized Jordan triple ▫$(\alpha, \beta)^\ast$▫-derivation on ▫$R$▫ is a generalized Jordan ▫$(\alpha, \beta)^\ast$▫-derivation. This result makes it possible to prove that every generalized Jordan triple ▫$(\alpha, \beta)^\ast$▫-derivation on a semisimple ▫$H^\ast$▫-algebra is a generalized Jordan ▫$(\alpha, \beta)^\ast$▫-derivation. Finally, we prove that every Jordan triple left ▫$\alpha^\ast$▫-centralizer on a 2-torsion free semiprime ring is a Jordan left ▫$\alpha^\ast$▫-centralizer.
Keywords: mathematics, algebra, semiprime ▫$\ast$▫-ring, ▫$H^\ast$▫-algebra, Jordan triple ▫$(\alpha, \beta)^\ast$▫-derivation, generalized Jordan triple ▫$(\alpha, \beta)^\ast$▫-derivation, Jordan triple left ▫$\alpha^\ast$▫-centralizer
Published in RUP: 15.10.2013; Views: 4438; Downloads: 77
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78. Identities with generalized skew derivations on Lie idealsVincenzo De Filippis, Ajda Fošner, Feng Wei, 2013, original scientific article Abstract: Let ▫$m, n$▫ be two nonzero fixed positive integers, ▫$R$▫ a 2-torsion free prime ring with the right Martindale quotient ring ▫$Q$▫, ▫$L$▫ a non-central Lie ideal of ▫$R$▫, and ▫$\delta$▫ a derivation of ▫$R$▫. Suppose that ▫$\alpha$▫ is an automorphism of ▫$R$▫, ▫$D$▫ a skew derivation of ▫$R$▫ with the associated automorphism ▫$\alpha$▫, and ▫$F$▫ a generalized skew derivation of ▫$R$▫ with the associated skew derivation ▫$D$▫. If ▫$$F(x^{m+n}) = F(x^m)x^n + x^m \delta (x^n)$$▫ is a polynomial identity for ▫$L$▫, then either ▫$R$▫ satisfies the standard polynomial identity ▫$s_4(x_1, x_2, x_3, x_4)$▫ of degree 4, or ▫$F$▫ is a generalized derivation of ▫$R$▫ and ▫$\delta = D$▫. Furthermore, in the latter case one of the following statements holds: (1) ▫$D = \delta = 0$▫ and there exists ▫$a \in Q$▫ such that ▫$F(x) = ax$▫ for all ▫$x \in R$▫; (2) ▫$\alpha$▫ is the identical mapping of ▫$R$▫.
Keywords: mathematics, algebra, polynomial identity, generalized skew derivation, prime ring
Published in RUP: 15.10.2013; Views: 4156; Downloads: 144
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