Generalized derivations in prime and semiprime
Let $R$ be a prime ring, $I$ a nonzero ideal of $R$ and $m, n$ fixed positive integers. If $R$ admits a generalized derivation $F$ associated with a nonzero derivation $d$ such that $(F([x,y])^{m}=[x,y]_{n}$ for all $x,y\in I$, then $R$ is commutative. Moreover we also examine the case when $R$...
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| Format: | Article |
| Language: | English |
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Sociedade Brasileira de Matemática
2016-05-01
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| Series: | Boletim da Sociedade Paranaense de Matemática |
| Subjects: | |
| Online Access: | http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/21774 |
| _version_ | 1811256781464141824 |
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| author | Shuliang Huang Nadeem ur Rehman |
| author_facet | Shuliang Huang Nadeem ur Rehman |
| author_sort | Shuliang Huang |
| collection | DOAJ |
| description | Let $R$ be a prime ring, $I$ a nonzero ideal of $R$ and $m, n$ fixed positive integers. If $R$ admits a generalized derivation $F$ associated with a nonzero derivation $d$ such that $(F([x,y])^{m}=[x,y]_{n}$ for all $x,y\in I$, then $R$ is commutative. Moreover we also examine the case when $R$ is a semiprime ring. |
| first_indexed | 2024-04-12T17:46:27Z |
| format | Article |
| id | doaj.art-b30e2be98627406f9aa4413b06e99ea5 |
| institution | Directory Open Access Journal |
| issn | 0037-8712 2175-1188 |
| language | English |
| last_indexed | 2024-04-12T17:46:27Z |
| publishDate | 2016-05-01 |
| publisher | Sociedade Brasileira de Matemática |
| record_format | Article |
| series | Boletim da Sociedade Paranaense de Matemática |
| spelling | doaj.art-b30e2be98627406f9aa4413b06e99ea52022-12-22T03:22:38ZengSociedade Brasileira de MatemáticaBoletim da Sociedade Paranaense de Matemática0037-87122175-11882016-05-01342293410.5269/bspm.v34i2.2177412363Generalized derivations in prime and semiprimeShuliang Huang0Nadeem ur Rehman1Chuzhou University, Chuzhou Anhui Department of MathematicsAligarh Muslim University Department of MathematicsLet $R$ be a prime ring, $I$ a nonzero ideal of $R$ and $m, n$ fixed positive integers. If $R$ admits a generalized derivation $F$ associated with a nonzero derivation $d$ such that $(F([x,y])^{m}=[x,y]_{n}$ for all $x,y\in I$, then $R$ is commutative. Moreover we also examine the case when $R$ is a semiprime ring.http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/21774prime and semiprime ringsgeneralized derivationsGPIs |
| spellingShingle | Shuliang Huang Nadeem ur Rehman Generalized derivations in prime and semiprime Boletim da Sociedade Paranaense de Matemática prime and semiprime rings generalized derivations GPIs |
| title | Generalized derivations in prime and semiprime |
| title_full | Generalized derivations in prime and semiprime |
| title_fullStr | Generalized derivations in prime and semiprime |
| title_full_unstemmed | Generalized derivations in prime and semiprime |
| title_short | Generalized derivations in prime and semiprime |
| title_sort | generalized derivations in prime and semiprime |
| topic | prime and semiprime rings generalized derivations GPIs |
| url | http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/21774 |
| work_keys_str_mv | AT shulianghuang generalizedderivationsinprimeandsemiprime AT nadeemurrehman generalizedderivationsinprimeandsemiprime |