Jordan homoderivation behavior of generalized derivations in prime rings
UDC 512.5 Suppose that $R$ is a prime ring with ${\rm char}(R)\neq 2$ and $f(\xi_1,\ldots,\xi_n)$ is a noncentral multilinear polynomial over $C( = Z(U)),$ where $U$ is the Utumi quotient ring of $R.$ An additive mapping $h\colon R\rightarrow R$ is called homoderivation if $h(ab) = h(a)...
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| Datum: | 2023 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2023
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/7241 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | UDC 512.5
Suppose that $R$ is a prime ring with ${\rm char}(R)\neq 2$ and $f(\xi_1,\ldots,\xi_n)$ is a noncentral multilinear polynomial over $C( = Z(U)),$ where $U$ is the Utumi quotient ring of $R.$ An additive mapping $h\colon R\rightarrow R$ is called homoderivation if $h(ab) = h(a)h(b)+h(a)b+ah(b)$ for all $a,b\in R.$ We investigate the behavior of three generalized derivations $F,$ $G,$ and $H$ of $R$ satisfying the condition $$F(\xi^2) = G(\xi)^2+H(\xi)\xi+\xi H(\xi)$$ for all $\xi \in f(R) = \{f(\xi_1,\ldots,\xi_n) \mid \xi_1,\ldots,\xi_n\in R\}.$ |
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| DOI: | 10.3842/umzh.v75i9.7241 |