Affiliation:
1. Faculty of Sciences Dhar El Mahraz , Sidi Mohamed Ben Abdellah University , Fez , Morocco
Abstract
Abstract
Let A and B be two associative rings, let I be an ideal of B and let
f
∈
Hom
(
A
,
B
)
{f\in\mathrm{Hom}(A,B)}
. In this paper, we give a complete description of generalized derivations over
A
⋈
f
I
{A\bowtie^{f}I}
. Furthermore, when A is prime or semi-prime, we give several identities on generalized derivations which provide the commutativity of
A
⋈
f
I
{A\bowtie^{f}I}
.
Reference14 articles.
1. E. Albaş,
Generalized derivations on ideals of prime rings,
Miskolc Math. Notes 14 (2013), no. 1, 3–9.
2. S. Ali, N. A. Dar and M. Asci,
On derivations and commutativity of prime rings with involution,
Georgian Math. J. 23 (2016), no. 1, 9–14.
3. M. Ashraf and N. ur Rehman,
On derivation and commutativity in prime rings,
East-West J. Math. 3 (2001), no. 1, 87–91.
4. M. D’Anna and M. Fontana,
An amalgamated duplication of a ring along an ideal: The basic properties,
J. Algebra Appl. 6 (2007), no. 3, 443–459.
5. M. D’Anna and M. Fontana,
The amalgamated duplication of a ring along a multiplicative-canonical ideal,
Ark. Mat. 45 (2007), no. 2, 241–252.