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Sibirskii Matematicheskii Zhurnal, 2006, Volume 47, Number 5, Pages 1052–1057
(Mi smj910)
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This article is cited in 25 scientific papers (total in 25 papers)
On Lie ideals with generalized derivations
Ö. Gölbaşia, K. Kayab a Cumhuriyet University
b Çanakkale Onsekiz Mart University
Abstract:
Let $R$ be a prime ring with characteristic different from 2, let $U$ be a nonzero Lie ideal of $R$, and let $f$ be a generalized derivation associated with $d$. We prove the following results: (i) If $a\in R$ and $[a,f(U)]=0$ then $a\in Z$ or $d(a)=0$ or $U\subset Z$; (ii) If $f^2(U)=0$ then $U\subset Z$; (iii) If $u^2\in U$ for all $u\in U$ and $f$ acts as a homomorphism or antihomomorphism on $U$ then either $d=0$ or $U\subset Z$.
Keywords:
derivation, Lie ideal, generalized derivation, homomorphism, antihomomorphism.
Received: 04.02.2005 Revised: 10.01.2006
Citation:
Ö. Gölbaşi, K. Kaya, “On Lie ideals with generalized derivations”, Sibirsk. Mat. Zh., 47:5 (2006), 1052–1057; Siberian Math. J., 47:5 (2006), 862–866
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https://www.mathnet.ru/eng/smj910 https://www.mathnet.ru/eng/smj/v47/i5/p1052
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Abstract page: | 407 | Full-text PDF : | 109 | References: | 73 |
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