Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON GENERALIZED (α, β)-DERIVATIONS AND COMMUTATIVITY IN PRIME RINGS

  • Published : 2006.02.01
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Abstract

Let R be a prime ring and I a nonzero ideal of R. Let $\alpha,\;\nu,\;\tau\;R{\rightarrow}R$ be the endomorphisms and $\beta,\;\mu\;R{\rightarrow}R$ the automorphisms. If R admits a generalized $(\alpha,\;\beta)-derivation$ g associated with a nonzero $(\alpha,\;\beta)-derivation\;\delta$ such that $g([\mu(x),y])\;=\;[\nu/(x),y]\alpha,\;\tau$ for all x, y ${\in}I$, then R is commutative.

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References

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