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,...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English English |
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Academic Publications
2013
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| Online Access: | http://psasir.upm.edu.my/id/eprint/30154/1/Prime%20gamma%20near.pdf |
| _version_ | 1796971683987324928 |
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| author | Rakhimov, Isamiddin Sattarovich Dey, Kalyan Kumar Paul, Akhil Chandra |
| author_facet | Rakhimov, Isamiddin Sattarovich Dey, Kalyan Kumar Paul, Akhil Chandra |
| author_sort | Rakhimov, Isamiddin Sattarovich |
| collection | UPM |
| description | 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}. |
| first_indexed | 2024-03-06T08:16:39Z |
| format | Article |
| id | upm.eprints-30154 |
| institution | Universiti Putra Malaysia |
| language | English English |
| last_indexed | 2024-03-06T08:16:39Z |
| publishDate | 2013 |
| publisher | Academic Publications |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | Rakhimov, Isamiddin Sattarovich Dey, Kalyan Kumar Paul, Akhil Chandra Prime gamma near-rings with derivations |
| title | 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_short | Prime gamma near-rings with derivations |
| title_sort | prime gamma near rings with derivations |
| url | http://psasir.upm.edu.my/id/eprint/30154/1/Prime%20gamma%20near.pdf |
| work_keys_str_mv | AT rakhimovisamiddinsattarovich primegammanearringswithderivations AT deykalyankumar primegammanearringswithderivations AT paulakhilchandra primegammanearringswithderivations |