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  • P-ISSN3059-0604
  • E-ISSN3059-1309
  • KCI

ISSN : 3059-0604

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Vol.14 No.4

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ON 4-PERMUTING 4-DERIVATIONS IN PRIME AND SEMIPRIME RINGS

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

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
2007, v.14 no.4, pp.271-278
Park, Kyoo-Hong (DEPARTMENT OF MATHEMATICS EDUCATION, SEOWON UNIVERSITY)
Park, Kyoo-Hong. (2007). ON 4-PERMUTING 4-DERIVATIONS IN PRIME AND SEMIPRIME RINGS. , 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

한국수학교육학회지시리즈B:순수및응용수학

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