Remarks on derivations on semiprime rings
We prove that a semiprime ring R must be commutative if it admits a derivation d such that (i) xy+d(xy)=yx+d(yx) for all x, y in R, or (ii) xy−d(xy)=yx−d(yx) for all x, y in R. In the event that R is prime, (i) or (ii) need only be assumed for all x, y in some nonzero ideal of R.
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
1992-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171292000255 |
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| _version_ | 1832558294541008896 |
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| author | Mohamad Nagy Daif Howard E. Bell |
| author_facet | Mohamad Nagy Daif Howard E. Bell |
| author_sort | Mohamad Nagy Daif |
| collection | DOAJ |
| description | We prove that a semiprime ring R must be commutative if it admits a derivation d such that (i) xy+d(xy)=yx+d(yx) for all x, y in R, or (ii) xy−d(xy)=yx−d(yx) for all x, y in R. In the event that R is prime, (i) or (ii) need only be assumed for all x, y in some nonzero ideal of R. |
| format | Article |
| id | doaj-art-1729dce66c4940ee9152f5aefc5bdda7 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1992-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-1729dce66c4940ee9152f5aefc5bdda72025-02-03T01:32:38ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251992-01-0115120520610.1155/S0161171292000255Remarks on derivations on semiprime ringsMohamad Nagy Daif0Howard E. Bell1Department of Mathematics, Faculty of Education, Umm Al-Qura University, Taif, Saudi ArabiaDepartment of Mathematics, Brock University, Ontario, St. Catharines, CanadaWe prove that a semiprime ring R must be commutative if it admits a derivation d such that (i) xy+d(xy)=yx+d(yx) for all x, y in R, or (ii) xy−d(xy)=yx−d(yx) for all x, y in R. In the event that R is prime, (i) or (ii) need only be assumed for all x, y in some nonzero ideal of R.http://dx.doi.org/10.1155/S0161171292000255derivationsemiprime ringprime ringcommutativecentral idealintegral domaindirect sum. |
| spellingShingle | Mohamad Nagy Daif Howard E. Bell Remarks on derivations on semiprime rings International Journal of Mathematics and Mathematical Sciences derivation semiprime ring prime ring commutative central ideal integral domain direct sum. |
| title | Remarks on derivations on semiprime rings |
| title_full | Remarks on derivations on semiprime rings |
| title_fullStr | Remarks on derivations on semiprime rings |
| title_full_unstemmed | Remarks on derivations on semiprime rings |
| title_short | Remarks on derivations on semiprime rings |
| title_sort | remarks on derivations on semiprime rings |
| topic | derivation semiprime ring prime ring commutative central ideal integral domain direct sum. |
| url | http://dx.doi.org/10.1155/S0161171292000255 |
| work_keys_str_mv | AT mohamadnagydaif remarksonderivationsonsemiprimerings AT howardebell remarksonderivationsonsemiprimerings |