Derivations in prime rings

Author:
B. Felzenszwalb

Journal:
Proc. Amer. Math. Soc. **84** (1982), 16-20

MSC:
Primary 16A72; Secondary 16A12

MathSciNet review:
633268

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Abstract: Let be a ring and a derivation of such that , , for all . It is shown that if is primitive then is an infinite field of characteristic and if . Moreover, if is prime and the set of integers is bounded, the same conclusion holds.

**[1]**I. N. Herstein,*On the hypercenter of a ring*, J. Algebra**36**(1975), 151-157. MR**0371962 (51:8179)****[2]**-,*On a resullt of Faith*, Canad. Math. Bull.**18**(1975), 609. MR**0393136 (52:13946)****[3]**-,*Rings with involution*, Univ. of Chicago Press, Chicago, Ill., 1976. MR**0442017 (56:406)****[4]**W. Martindale,*Prime rings satisfying a generalized polynomial identity*, J. Algebra**12**(1969), 576-584. MR**0238897 (39:257)****[5]**M. Smith,*Rings with an integral element whose centralizer satisfies a polynomial identity*, Duke Math. J.**42**(1975), 137-149. MR**0399156 (53:3007)**

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1982-0633268-6

Article copyright:
© Copyright 1982
American Mathematical Society