$b$ -Generalized derivations on prime rings
Let $R$ be a prime ring with center $Z(R)$, right Martindale quotient ring $Q$ and extended centroid $C$. By a $b$-generalized derivation we mean an additive mapping $g:R\rightarrow Q$ such that $g(xy) = g(x)y + bxd(y)$ for all $x,y \in R$, where $b \in Q$ and $d: R \rightarrow Q$ is an additive map...
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| Datum: | 2022 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2022
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/5989 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | Let $R$ be a prime ring with center $Z(R)$, right Martindale quotient ring $Q$ and extended centroid $C$. By a $b$-generalized derivation we mean an additive mapping $g:R\rightarrow Q$ such that $g(xy) = g(x)y + bxd(y)$ for all $x,y \in R$, where $b \in Q$ and $d: R \rightarrow Q$ is an additive map. In this paper, we extend some well-known results concerning (generalized) derivations on prime rings to $b$-generalized derivations. Further we investigate $b$-generalized derivation acting as a homomorphism or anti-homomorphism in a prime ring. |
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| DOI: | 10.37863/umzh.v74i6.5989 |