Prime gamma-near-rings with (σ, τ)-derivations
Let N be a 2 torsion free prime Γ-near-ring with center Z(N) and let d be a nontrivial derivation on N such that d(N) ⊆ Z(N). Then we prove that N is commutative. Also we prove that if d be a nonzero (σ,τ)-derivation on N such that d(N) commutes with an element aofN then ether d is trivial or a is i...
| 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/30155/1/Prime%20gamma.pdf |
| _version_ | 1796971684186554368 |
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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 2 torsion free prime Γ-near-ring with center Z(N) and let d be a nontrivial derivation on N such that d(N) ⊆ Z(N). Then we prove that N is commutative. Also we prove that if d be a nonzero (σ,τ)-derivation on N such that d(N) commutes with an element aofN then ether d is trivial or a is in Z(N). Finally if d1 be a nonzero (σ,τ)-derivation and d2 be a nonzero derivation on N such that d1τ = τ d1, d1σ = σd1, d2τ = τ d2, d2σ = σd2 with d1(N)Γσ(d2(N)) = τ(d2(N))Γd1(N) then N is a commutative Γ-ring. |
| first_indexed | 2024-03-06T08:16:39Z |
| format | Article |
| id | upm.eprints-30155 |
| 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-301552015-10-30T03:17:55Z http://psasir.upm.edu.my/id/eprint/30155/ Prime gamma-near-rings with (σ, τ)-derivations Rakhimov, Isamiddin Sattarovich Dey, Kalyan Kumar Paul, Akhil Chandra Let N be a 2 torsion free prime Γ-near-ring with center Z(N) and let d be a nontrivial derivation on N such that d(N) ⊆ Z(N). Then we prove that N is commutative. Also we prove that if d be a nonzero (σ,τ)-derivation on N such that d(N) commutes with an element aofN then ether d is trivial or a is in Z(N). Finally if d1 be a nonzero (σ,τ)-derivation and d2 be a nonzero derivation on N such that d1τ = τ d1, d1σ = σd1, d2τ = τ d2, d2σ = σd2 with d1(N)Γσ(d2(N)) = τ(d2(N))Γd1(N) then N is a commutative Γ-ring. Academic Publications 2013 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/30155/1/Prime%20gamma.pdf Rakhimov, Isamiddin Sattarovich and Dey, Kalyan Kumar and Paul, Akhil Chandra (2013) Prime gamma-near-rings with (σ, τ)-derivations. International Journal of Pure and Applied Mathematics, 82 (5). pp. 669-681. ISSN 1311-8080; ESSN: 1314-3395 http://www.ijpam.eu/contents/2013-82-5/index.html English |
| spellingShingle | Rakhimov, Isamiddin Sattarovich Dey, Kalyan Kumar Paul, Akhil Chandra Prime gamma-near-rings with (σ, τ)-derivations |
| title | Prime gamma-near-rings with (σ, τ)-derivations |
| title_full | Prime gamma-near-rings with (σ, τ)-derivations |
| title_fullStr | Prime gamma-near-rings with (σ, τ)-derivations |
| title_full_unstemmed | Prime gamma-near-rings with (σ, τ)-derivations |
| title_short | Prime gamma-near-rings with (σ, τ)-derivations |
| title_sort | prime gamma near rings with σ τ derivations |
| url | http://psasir.upm.edu.my/id/eprint/30155/1/Prime%20gamma.pdf |
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