Higher Derivations on Lie Ideals

C. HAETINGER

Abstract


In this paper we present a brief proof of a recently proved result [5, Corollary 1.4]. The main result states that if R is a prime ring of characteristic different of 2 and U is a Lie ideal of R where U 6½ Z(R), the center of R, u2 2 U for all u 2 U, and D is a Jordan higher derivation of U into R, then D is a higher derivation of U into R. This result extends a theorem of Awtar [1].

References


[1] R. Awtar, Lie ideals and Jordan derivations of prime rings, Proc. Amer. Math. Soc., 90, No. 1 (1984), 9-14.

J. Bergen, I. N . Herstein and J. W. Kerr, Lie ideals and derivations of prime rings, J. Algebra, 71 (1981), 259-267.

D. R. Farkas, C. Geiss and E. N. Marcos, Smooth automorphism group schemes, in “Conference on Representations of Algebras”, São Paulo, Brazil, to appear.

M. Ferrero and C. Haetinger, Higher derivations of semiprime rings, Comm. Algebra, to appear.

M. Ferrero and C. Haetinger, Higher derivations and a theorem by Herstein, Quaestiones Mathematicae, to appear.

C. Haetinger, “Derivações de Ordem Superior em Anéis Primos e Semiprimos”, Ph.D. thesis, IMUFRGS, UFRGS, Porto Alegre, RS, Brazil, 2000.

I. N. Herstein, Jordan derivations of prime rings, Proc. Amer. Math. Soc., 8 (1957), 1104-1110.

C. Lanski and S. Montgomery, Lie structure of prime rings of characteristic 2, Pacific J. Math., 42, No. 1 (1972), 117-136.




DOI: https://doi.org/10.5540/tema.2002.03.01.0141

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