Identities with generalized skew derivations on Lie ideals

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Language:	English
Year of publishing:	2013
Typology:	1.01 - Original Scientific Article
Organization:	UP - University of Primorska
UDC:	512.552
COBISS:	16653657
ISSN:	1386-923X
Views:	3853
Downloads:	144
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Secondary language:	Slovenian
Secondary title:	Identitete s posplošenimi [alpha]-odvajanji na Lijevih idealih
Secondary 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 ▫$R$▫.
Secondary keywords:	matematika;algebra;polinomska identiteta;prakolobar;posplošeno ▫$\alpha▫-odvajanje;
Type (COBISS):	Not categorized
Pages:	str. 1017-1038
Volume:	ǂVol. ǂ16
Issue:	ǂiss. ǂ4
Chronology:	2013
ID:	1476884