Identities with generalized skew derivations on Lie ideals

De Filippis, Vincenzo; Fošner, Ajda; Wei, Feng

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Title:	Identities with generalized skew derivations on Lie ideals
Authors:	ID De Filippis, Vincenzo (Author) ID Fošner, Ajda (Author) ID Wei, Feng (Author)
Files:	http://dx.doi.org/10.1007/s10468-012-9344-4
Language:	English
Work type:	Not categorized
Typology:	1.01 - Original Scientific Article
Organization:	IAM - Andrej Marušič Institute
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
Year of publishing:	2013
Number of pages:	str. 1017-1038
Numbering:	Vol. 16, issue 4
PID:	20.500.12556/RUP-1000
ISSN:	1386-923X
UDC:	512.552
COBISS.SI-ID:	16653657
Publication date in RUP:	15.10.2013
Views:	5485
Downloads:	147
Metadata:
:	DE FILIPPIS, Vincenzo, FOŠNER, Ajda and WEI, Feng, 2013, Identities with generalized skew derivations on Lie ideals. [online]. 2013. Vol. 16, no. 4, p. 1017–1038. [Accessed 22 April 2025]. Retrieved from: http://dx.doi.org/10.1007/s10468-012-9344-4 Copy citation

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Secondary language

Language:	Slovenian
Abstract:	V članku je obravnavana posebna identiteta na Liejevem idealu prakolobarja, ki vklučuje posplošeno $\alpha$ -odvajanje.
Keywords:	matematika, algebra, polinomska identiteta, prakolobar, posplošeno ▫$\alpha▫-odvajanje

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