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,...
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2013
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| 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 |
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my.upm.eprints.301542015-10-30T03:16:43Z http://psasir.upm.edu.my/id/eprint/30154/ Prime gamma near-rings with derivations Rakhimov, Isamiddin Sattarovich Dey, Kalyan Kumar Paul, Akhil Chandra 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}. Academic Publications 2013 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/30154/1/Prime%20gamma%20near.pdf Rakhimov, Isamiddin Sattarovich and Dey, Kalyan Kumar and Paul, Akhil Chandra (2013) Prime gamma near-rings with derivations. International Journal of Pure and Applied Mathematics, 83 (2). pp. 221-231. ISSN 1311-8080; ESSN: 1314-3395 http://www.ijpam.eu/contents/2013-83-2/index.html English |
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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}. |
| format |
Article |
| author |
Rakhimov, Isamiddin Sattarovich Dey, Kalyan Kumar Paul, Akhil Chandra |
| spellingShingle |
Rakhimov, Isamiddin Sattarovich Dey, Kalyan Kumar Paul, Akhil Chandra Prime gamma near-rings with derivations |
| author_facet |
Rakhimov, Isamiddin Sattarovich Dey, Kalyan Kumar Paul, Akhil Chandra |
| author_sort |
Rakhimov, Isamiddin Sattarovich |
| title |
Prime gamma near-rings with derivations |
| title_short |
Prime gamma near-rings with derivations |
| title_full |
Prime gamma near-rings with derivations |
| title_fullStr |
Prime gamma near-rings with derivations |
| title_full_unstemmed |
Prime gamma near-rings with derivations |
| title_sort |
prime gamma near-rings with derivations |
| publisher |
Academic Publications |
| publishDate |
2013 |
| url |
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 |
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