Action of multiplicative (generalized)-derivations and related maps on square closed Lie ideals in prime rings
Let $\mathcal{R}$ be a prime ring and $L$ a nonzero square closed Lie ideal of $\mathcal{R}$. Suppose $F,G,H\colon \mathcal{R}\to \mathcal{R}$\break are three multiplicative (generalized)-derivations associated with the maps $\delta,g, h\colon \mathcal{R}\to \mathcal{R}$ respectively which are not n...
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| Format: | Article |
| Language: | German |
| Published: |
Ivan Franko National University of Lviv
2025-03-01
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| Series: | Математичні Студії |
| Subjects: | |
| Online Access: | http://matstud.org.ua/ojs/index.php/matstud/article/view/544 |
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| Summary: | Let $\mathcal{R}$ be a prime ring and $L$ a nonzero square closed Lie ideal of $\mathcal{R}$. Suppose $F,G,H\colon \mathcal{R}\to \mathcal{R}$\break are three multiplicative (generalized)-derivations associated with the maps $\delta,g, h\colon \mathcal{R}\to \mathcal{R}$ respectively which are not necessarily additive or derivations. Assume that $E,T\colon \mathcal{R}\to \mathcal{R}$ be any two maps (not necessarily additive).
Let $d\colon \mathcal{R}\to \mathcal{R}$ be a nonzero derivation of $\mathcal{R}$. In the present article, following identities are studied
(1) $d(x)F(y)+G(y)d(x)\pm (E(x)y+yT(u))=0,\quad$ $(2)\ H(xy)+G(y)F(x)\pm (E(y)x+xT(y))=0$,
(3) $T(xy)+G(x)y\pm (yx+xy)=0, \quad$ $(4)\ F(x)F(y)+T(x)y\pm yx=0,$ (5) $d(x)d(y)+T(x)y+F(yx)=0$, for all $x,y\in L$. |
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| ISSN: | 1027-4634 2411-0620 |