A NOTE ON LIE IDEALS OF PRIME RINGS
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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.
Abstract
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.
참고문헌 (9)
- M. Ashraf, "On derivations in rings and their applications", Aligarh Bull. Math., 25(2), pp.79~107 (2006)
- R. Awtar, "Lie structure in prime rings with derivations", Publ. Math. Debrecen, 31(3), pp.209~215 (1984)
- R. Awtar, "Lie ideals and Jordan derivations of prime rings", Proc. Amer. Math. Soc., 90(1), pp.9~14 (1984)
- J. Bergen, "Lie ideals and derivations of prime rings", J. Algebra, 71(1), pp.259~267 (1981)
- C. Haetinger, "Higher derivations on Lie ideals", TEMA Tend. Mat. Apl. Comput., 3(1), pp.141~145 (2002)
- P. H. Lee, "Lie ideals of prime rings with derivations", Bull. Inst. Math. Acad. Sinica, 11(1), pp.75~80 (1983)
- F. W. Niu, "On a pair of derivations on associative rings", J. Math. (Wuhan), 10(4), pp.385~390 (1990)
- E. C. Posner, "Derivations in prime rings", Proc. Amer. Math. Soc., 통권 : 8, pp.1093~1100 (1957)
- J. Vukman, "Commuting and centralizing mappings in prime rings", Proc. Amer. Math. Soc., 109(1), pp.47~52 (1990)