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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Hindawi Limited
1997-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171297000562 |
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doaj-6cf624c965a8448a90d981197b9ac4c32020-11-24T22:04:19ZengHindawi LimitedInternational 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. |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Motoshi Hongan |
| spellingShingle |
Motoshi Hongan A note on semiprime rings with derivation International Journal of Mathematics and Mathematical Sciences derivation semiprime ring 2-torsion free ring. |
| author_facet |
Motoshi Hongan |
| author_sort |
Motoshi Hongan |
| title |
A note on semiprime rings with derivation |
| title_short |
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_sort |
note on semiprime rings with derivation |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
1997-01-01 |
| 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. |
| 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 |
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1725829403517124608 |