- 期刊
COMMUTATIVITY RESULTS FOR SEMIPRIME RINGS WITH DERIVATIONS
摘要
We extend a result of Herstein co,cerning 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.
延伸閱讀
- LUH, J., & YE, Y. (1998). DERIVATIONS OF HIGHER ORDER IN SEMIPRIME RINGS. International Journal of Mathematics and Mathematical Sciences, 1998(), 89-92. https://doi.org/10.1155/S0161171298000106
- Shuliang, H. (2007). Generalized Derivations of Prime Rings. International Journal of Mathematics and Mathematical Sciences, 2007(), 1199-1204. https://doi.org/10.1155/2007/85612
- BELL, H. E., & GUERRIERO, F. (1990). SOME CONDITIONS FOR FINITENESS AND COMMUTATIVITY OF RINGS. International Journal of Mathematics and Mathematical Sciences, 1990(), 535-544. https://doi.org/10.1155/S0161171290000771
- KLEIN, A. A., & BELL, H. E. (2004). A COMMUTATIVITY-OR-FINITENESS CONDITION FOR RINGS. International Journal of Mathematics and Mathematical Sciences, 2004(), 2863-2865-220. https://doi.org/10.1155/S0161171204405420
- Dhara, B., & Pattanayak, A. (2012). On Generalized (σ, τ)-Derivations in Semiprime Rings. ISRN Algebra, (), 3-9. https://doi.org/10.5402/2012/120251