Commutativity results for semiprime rings with derivations
We extend a result of Herstein concerning a derivation d on a prime ring R satisfying [d(x),d(y)]=0 for all x,y∈R, to the case of semiprime rings. An extension of this result is proved for a two-sided ideal but is shown to be not true for a one-sided ideal. Some of our recent results dealing with U...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1998-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171298000660 |
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| Summary: | We extend a result of Herstein concerning a derivation d on a prime ring R satisfying
[d(x),d(y)]=0
for all x,y∈R, to the case of semiprime rings. An extension of this result is proved for
a two-sided ideal but is shown to be not true for a one-sided ideal. Some of our recent results dealing
with U*- and U**- derivations on a prime ring are extended to semiprime rings. Finally, we obtain a
result on semiprime rings for which d(xy)=d(yx) for all x,y in some ideal U. |
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| ISSN: | 0161-1712 1687-0425 |