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Let R be a 2-torsion free prime ring, U a nonzero Lie ideal of R such that u2 ε U for all u ε U. In the present paper, it is proved that if d is a nonzero derivation and [[d(u), u], u] = 0 for all u ε U, then U ⊆ Z(R). Moreover, suppose that d1, d2, d3 are nonzero derivations of R such that d3(y)d1(x) = d2(x)d3(y) for all x, y ε U, then U ⊆ Z(R).
Finally, some examples are given to demonstrate that the restrictions imposed on the hypothesis of the above results are not superfluous.
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참고문헌 (9)
참고문헌 신청
C. Haetinger / 2002 / Higher derivations on Lie ideals / TEMA Tend. Mat. Apl. Comput. 3 (1) : 141 ~ 145
E. C. Posner / 1957 / Derivations in prime rings / Proc. Amer. Math. Soc. : 1093 ~ 1100
F. W. Niu / 1990 / On a pair of derivations on associative rings / J. Math. (Wuhan) 10 (4) : 385 ~ 390
J. Bergen / 1981 / Lie ideals and derivations of prime rings / J. Algebra 71 (1) : 259 ~ 267
J. Vukman / 1990 / Commuting and centralizing mappings in prime rings / Proc. Amer. Math. Soc. 109 (1) : 47 ~ 52
E. C. Posner / 1957 / Derivations in prime rings / Proc. Amer. Math. Soc. : 1093 ~ 1100
F. W. Niu / 1990 / On a pair of derivations on associative rings / J. Math. (Wuhan) 10 (4) : 385 ~ 390
J. Bergen / 1981 / Lie ideals and derivations of prime rings / J. Algebra 71 (1) : 259 ~ 267
J. Vukman / 1990 / Commuting and centralizing mappings in prime rings / Proc. Amer. Math. Soc. 109 (1) : 47 ~ 52
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