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 |
| Published: |
Academic Publications
2013
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| Online Access: | http://psasir.upm.edu.my/id/eprint/30155/1/Prime%20gamma.pdf |
| Summary: | 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. |
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