Derivations with nilpotent values on Lie ideals

Author:
Charles Lanski

Journal:
Proc. Amer. Math. Soc. **108** (1990), 31-37

MSC:
Primary 16A72; Secondary 16A12, 16A68

MathSciNet review:
984803

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Abstract: Let be a ring containing no nonzero nil right ideal and let be a Lie ideal of . If is a derivation of so that is a nilpotent element for each , then when is a prime ring and is not commutative. The main result shows that in general, for the ideal generated by and that is the subdirect sum of two images so that induces the zero derivation on one, and the image of in the other is commutative.

**[1]**L. Carini and A. Giambruno,*Lie ideals and nil derivations*, Boll. Un. Mat. Ital. A (6)**4**(1985), no. 3, 497–503 (English, with Italian summary). MR**821089****[2]**B. Felzenszwalb and Charles Lanski,*On the centralizers of ideals and nil derivations*, J. Algebra**83**(1983), no. 2, 520–530. MR**714263**, 10.1016/0021-8693(83)90237-5**[3]**A. Giambruno and I. N. Herstein,*Derivations with nilpotent values*, Rend. Circ. Mat. Palermo (2)**30**(1981), no. 2, 199–206. MR**651152**, 10.1007/BF02844306**[4]**I. N. Herstein,*Topics in ring theory*, The University of Chicago Press, Chicago, Ill.-London, 1969. MR**0271135****[5]**I. N. Herstein,*Invariant subrings of a certain kind*, Israel J. Math.**26**(1977), no. 2, 205–208. MR**0432711****[6]**I. N. Herstein,*Center-like elements in prime rings*, J. Algebra**60**(1979), no. 2, 567–574. MR**549949**, 10.1016/0021-8693(79)90102-9**[7]**Charles Lanski and Susan Montgomery,*Lie structure of prime rings of characteristic 2*, Pacific J. Math.**42**(1972), 117–136. MR**0323839**

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1990-0984803-4

Article copyright:
© Copyright 1990
American Mathematical Society