Generalized derivations and commuting additive maps on multilinear polynomials in prime rings
Let $R$ be a prime ring with characteristic different from $2, U$ be its right Utumi quotient ring, $C$ be its extended centroid, $F$ and $G$ be additive maps on $R$ , $f(x_1, ..., x_n)$ be a multilinear polynomial over $C$, and $I$ be a nonzero right ideal of $R$ . We obtain information about the...
Збережено в:
| Дата: | 2016 |
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| Автори: | , , , , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2016
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/1833 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | Let $R$ be a prime ring with characteristic different from $2, U$ be its right Utumi quotient ring, $C$ be its extended centroid, $F$ and $G$ be additive maps on $R$ , $f(x_1, ..., x_n)$ be a multilinear polynomial over $C$, and $I$ be a nonzero right ideal of $R$ .
We obtain information about the structure of $R$ and describe the form of $F$ and $G$ in the following cases:
$$(1) [(F^2 + G)(f(r_1, ..., r_n)), f(r_1, ..., r_n)] = 0$$ for all $r_1, . . . , r_n \in R$, where $F$ and $G$ are generalized derivations of $R$ ;
$$(2) [(F^2 + G)(f(r_1, ..., r_n)), f(r_1, ..., r_n)] = 0$$for all $r_1, ..., r_n \in I$, where $F$ and $G$ are derivations of $R$. |
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