Let $R$ be a prime ring, $I$ a nonzero ideal of $R$ and $m, n$ fixed positive integers. If $R$ admits a generalized derivation $F$ associated with a nonzero derivation $d$ such that $(F([x,y])^{m}=[x,y]_{n}$ for all $x,y\in I$, then $R$ is commutative. Moreover we also examine the case when $R$ is a semiprime ring.
@article{21774,
title = {Generalized derivations in prime and semiprime},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {34},
year = {2015},
doi = {10.5269/bspm.v34i2.21774},
language = {EN},
url = {http://dml.mathdoc.fr/item/21774}
}
Huang, Shuliang; Rehman, Nadeem ur. Generalized derivations in prime and semiprime. Boletim da Sociedade Paranaense de Matemática, Tome 34 (2015) . doi : 10.5269/bspm.v34i2.21774. http://gdmltest.u-ga.fr/item/21774/