20.500.12556/RUP-1000 Identities with generalized skew derivations on Lie ideals 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 ▫$R$▫. V članku je obravnavana posebna identiteta na Liejevem idealu prakolobarja, ki vklučuje posplošeno ▫$\alpha$▫-odvajanje. mathematics algebra polynomial identity generalized skew derivation prime ring matematika algebra polinomska identiteta prakolobar posplošeno ▫$\alpha▫-odvajanje true true false Angleški jezik Slovenski jezik Delo ni kategorizirano 2013-10-15 12:05:28 2013-10-15 12:05:28 2024-03-01 11:59:34 0000-00-00 00:00:00 2013 0 0 str. 1017-1038 issue 4 Vol. 16 2013 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 1386-923X 512.552 16653657 http://dx.doi.org/10.1007/s10468-012-9344-4 1 https://repozitorij.upr.si/Dokument.php?lang=slv&id=1000 Inštitut Andrej Marušič 0 0 0