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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.14 No.4

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On 4-permuting 4-derivations in Prime and Semiprime Rings

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2007, v.14 no.4, pp.271-278
Park, Kyoo-Hong
Park,, K. (2007). On 4-permuting 4-derivations in Prime and Semiprime Rings. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 14(4), 271-278.

Abstract

Let R be a 2-torsion free semiprime ring. Suppose that there exists a 4-permuting 4-derivation <TEX>${\Delta}:R{\times}R{\times}R{\times}R{\rightarrow}R$</TEX> such that the trace is centralizing on R. Then the trace of <TEX>${\Delta}$</TEX> is commuting on R. In particular, if R is a 3!-torsion free prime ring and <TEX>${\Delta}$</TEX> is nonzero under the same condition, then R is commutative.

keywords
prime ring, semiprime ring, commuting map, centralizing map, n-permuting map, derivation, 4-derivation

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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