| Title: | Identities with generalized skew derivations on Lie ideals |
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| Authors: | ID De Filippis, Vincenzo (Author)
ID Fošner, Ajda (Author)
ID Wei, Feng (Author) |
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| Files: |  http://dx.doi.org/10.1007/s10468-012-9344-4
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| Language: | English |
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| Work type: | Not categorized |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | IAM - Andrej Marušič Institute
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| 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 ▫$R$▫. |
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| Keywords: | mathematics, algebra, polynomial identity, generalized skew derivation, prime ring |
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| Year of publishing: | 2013 |
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| Number of pages: | str. 1017-1038 |
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| Numbering: | Vol. 16, issue 4 |
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| PID: | 20.500.12556/RUP-1000  |
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| ISSN: | 1386-923X |
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| UDC: | 512.552 |
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| COBISS.SI-ID: | 16653657 |
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| Publication date in RUP: | 15.10.2013 |
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| Views: | 4953 |
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| Downloads: | 145 |
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