A note on semiprime rings with derivation
Let R be a 2-torsion free semiprime ring, I a nonzero ideal of R, Z the center of R and D:R→R a derivation. If d[x,y]+[x,y]∈Z or d[x,y]−[x,y]∈Z for all x, y∈I, then R is commutative.
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| Format: | Article |
| Language: | English |
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Wiley
1997-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171297000562 |
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| _version_ | 1832555863666065408 |
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| author | Motoshi Hongan |
| author_facet | Motoshi Hongan |
| author_sort | Motoshi Hongan |
| collection | DOAJ |
| description | Let R be a 2-torsion free semiprime ring, I a nonzero ideal of R, Z the center
of R and D:R→R a derivation. If d[x,y]+[x,y]∈Z or d[x,y]−[x,y]∈Z for all x, y∈I,
then R is commutative. |
| format | Article |
| id | doaj-art-6cf624c965a8448a90d981197b9ac4c3 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1997-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-6cf624c965a8448a90d981197b9ac4c32025-02-03T05:46:58ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251997-01-0120241341510.1155/S0161171297000562A note on semiprime rings with derivationMotoshi Hongan0Tsuyama College of Technology Numa, Tsuyama, Okayama 708, JapanLet R be a 2-torsion free semiprime ring, I a nonzero ideal of R, Z the center of R and D:R→R a derivation. If d[x,y]+[x,y]∈Z or d[x,y]−[x,y]∈Z for all x, y∈I, then R is commutative.http://dx.doi.org/10.1155/S0161171297000562derivationsemiprime ring2-torsion free ring. |
| spellingShingle | Motoshi Hongan A note on semiprime rings with derivation International Journal of Mathematics and Mathematical Sciences derivation semiprime ring 2-torsion free ring. |
| title | A note on semiprime rings with derivation |
| title_full | A note on semiprime rings with derivation |
| title_fullStr | A note on semiprime rings with derivation |
| title_full_unstemmed | A note on semiprime rings with derivation |
| title_short | A note on semiprime rings with derivation |
| title_sort | note on semiprime rings with derivation |
| topic | derivation semiprime ring 2-torsion free ring. |
| url | http://dx.doi.org/10.1155/S0161171297000562 |
| work_keys_str_mv | AT motoshihongan anoteonsemiprimeringswithderivation AT motoshihongan noteonsemiprimeringswithderivation |