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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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Let m, n, r be nonzero fixed positive integers, R a 2-torsion free prime ring, Q its right Martindale quotient ring, and L a non-central Lie ideal of R. Let D : $R{\rightarrow}R$ be a skew derivation of R and $E(x)=D(x^{m+n+r})-D(x^m)x^{n+r}-x^mD(x^n)x^r-x^{m+n}D(x^r)$. We prove that if $E(x)=0$ for all $x{\in}L$, then D is a usual derivation of R or R satisfies $s_4(x_1,{\ldots},x_4)$, the standard identity of degree 4.
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참고문헌 (12)
참고문헌 신청
B. Dhara / 2011 / Generalized derivations and left multipliers on Lie ideals / Aequationes Math 81 : 251 ~ 261
C. Lanski / 1988 / Differential identities, Lie ideals, and Posner's theorems / Pacific J. Math 134 (2) : 275 ~ 297
C.-L. Chuang / 1988 / GPIs having coefficients in Utumi quotient rings / Proc. Amer. Math. Soc 103 (3) : 723 ~ 728
C.-L. Chuang / 1992 / Differential identities with automorphisms and antiautomorphisms I / J. Algebra 149 (2) : 371 ~ 404
C.-L. Chuang / 1993 / Differential identities with automorphisms and antiautomorphisms II / J. Alge- bra 160 (1) : 130 ~ 171
C. Lanski / 1988 / Differential identities, Lie ideals, and Posner's theorems / Pacific J. Math 134 (2) : 275 ~ 297
C.-L. Chuang / 1988 / GPIs having coefficients in Utumi quotient rings / Proc. Amer. Math. Soc 103 (3) : 723 ~ 728
C.-L. Chuang / 1992 / Differential identities with automorphisms and antiautomorphisms I / J. Algebra 149 (2) : 371 ~ 404
C.-L. Chuang / 1993 / Differential identities with automorphisms and antiautomorphisms II / J. Alge- bra 160 (1) : 130 ~ 171
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