Let R be a ring and F and G be generalized derivations ofR with associated derivations d and g respectively. In the present paper,we shall investigate the commutativity of semiprime ring R admitting generalizedderivations F and G satisfying any one of the properties: (i)F(x)x =xG(x); (ii) [F(x); d(y)] = [x; y]; (iii) F([x; y]) = [d(x); F(y)]; (iv) d(x)F(y) =xy; (v) F(x2) = x2; (vi) [F(x); y] = [x;G(y)]; (vii) F([x; y]) = [F(x); y]+[d(y); x] and(viii) F(x ◦ y) = F(x) ◦ y − d(y) ◦ x for all x; y in some appropriate subset of R.
@article{10649,
title = {On Semiprime Rings with Generalized Derivations - doi: 10.5269/bspm.v28i2.10649},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {28},
year = {2010},
doi = {10.5269/bspm.v28i2.10649},
language = {EN},
url = {http://dml.mathdoc.fr/item/10649}
}
Rehman, Nadeem ur; Ashraf, Mohammad; Ali, Shakir; Mozumder, Muzibur Rahman. On Semiprime Rings with Generalized Derivations - doi: 10.5269/bspm.v28i2.10649. Boletim da Sociedade Paranaense de Matemática, Tome 28 (2010) . doi : 10.5269/bspm.v28i2.10649. http://gdmltest.u-ga.fr/item/10649/