On Semiprime Rings with Generalized Derivations - doi: 10.5269/bspm.v28i2.10649

Nadeem ur Rehman; Mohammad Ashraf; Shakir Ali; Muzibur Rahman Mozumder

doi:10.5269/bspm.v28i2.10649

Auteurs-es

Nadeem ur Rehman Aligarh Muslim University
Mohammad Ashraf Aligarh Muslim University
Shakir Ali Aligarh Muslim University
Muzibur Rahman Mozumder Aligarh Muslim University

DOI :

https://doi.org/10.5269/bspm.v28i2.10649

Mots-clés :

Ideal, semiprime ring, derivation, generalized derivation, commutativity.

Résumé

Let R be a ring and F and G be generalized derivations of
R with associated derivations d and g respectively. In the present paper,
we shall investigate the commutativity of semiprime ring R admitting generalized
derivations 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 â—¦ y) = F(x) â—¦ y − d(y) â—¦ x for all x; y in some appropriate subset of R.