Prime gamma near-rings with derivations
Let N be a prime Γnear-ring with the center Z(N). The objective of this paper is to study derivations on N. We prove two results: (a) Let N be 2-torsion free and let D1 and D2 be derivations on N such that D1D2 is also a derivation. Then D1 = 0 or D2 = 0 if and only if[D1(x), D2(y)]α = 0 for all x,...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English English |
| Published: |
Academic Publications
2013
|
| Online Access: | http://psasir.upm.edu.my/id/eprint/30154/1/Prime%20gamma%20near.pdf http://psasir.upm.edu.my/id/eprint/30154/ http://www.ijpam.eu/contents/2013-83-2/index.html |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | Let N be a prime Γnear-ring with the center Z(N). The objective of this paper is to study derivations on N. We prove two results:
(a) Let N be 2-torsion free and let D1 and D2 be derivations on N such that D1D2 is also a derivation. Then D1 = 0 or D2 = 0 if and only if[D1(x), D2(y)]α = 0 for all x, y ∈ N, α ∈ Γ;
b) Let n be an integer greater than 1, N be n!-torsion free, and D be a derivation with Dn(N) = {0}. Then D(Z(N)) = {0}. |
|---|