Identities on additive mappings in semiprime rings
Consider a ring $R$, which is semiprime and also having $k$-torsion freeness. If $F, d : R\to R$ are two additive maps fulfilling the algebraic identity $$F(x^{n+m})=F(x^m) x^n+ x^m d(x^n)$$ for each $x$ in $R.$ Then $F$ will be a generalized derivation having $d$ as an associated derivation on $R$....
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| Main Authors: | , |
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| Format: | Article |
| Language: | German |
| Published: |
Ivan Franko National University of Lviv
2023-01-01
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| Series: | Математичні Студії |
| Subjects: | |
| Online Access: | http://matstud.org.ua/ojs/index.php/matstud/article/view/317 |
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| Summary: | Consider a ring $R$, which is semiprime and also having $k$-torsion freeness. If $F, d : R\to R$ are two additive maps fulfilling the algebraic identity $$F(x^{n+m})=F(x^m) x^n+ x^m d(x^n)$$ for each $x$ in $R.$ Then $F$ will be a generalized derivation having $d$ as an associated derivation on $R$. On the other hand, in this article, it is also derived that $f$ is a generalized left derivation having a linked left derivation $\delta$ on $R$ if they satisfy the algebraic identity $$f(x^{n+m})=x^n f(x^m)+ x^m \delta(x^n)$$ for each $x$ in $R$ and $k\in \{2, m, n, (n+m-1)!\}$ and at last an application on Banach algebra is presented. |
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| ISSN: | 1027-4634 2411-0620 |