Nil derivations and chain conditions in prime rings
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- by L. O. Chung and Y. Kobayashi PDF
- Proc. Amer. Math. Soc. 94 (1985), 201-205 Request permission
Abstract:
It is known that in a prime ring, a derivation nilpotent on a nonzero ideal must also be nilpotent in the entire ring. In this paper we show that a derivation of a prime ring is not necessarily nil even though it is nil on a nonzero ideal. It is nil if the ring satisfies the ascending chain condition on left (right) annihilator ideals.References
- A. W. Chatters and C. R. Hajarnavis, Rings with chain conditions, Research Notes in Mathematics, vol. 44, Pitman (Advanced Publishing Program), Boston, Mass.-London, 1980. MR 590045
- L. O. Chung, Nil derivations, J. Algebra 95 (1985), no. 1, 20–30. MR 797651, DOI 10.1016/0021-8693(85)90089-4
- L. O. Chung and Jiang Luh, Nilpotency of derivations, Canad. Math. Bull. 26 (1983), no. 3, 341–346. MR 703409, DOI 10.4153/CMB-1983-057-5
Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 94 (1985), 201-205
- MSC: Primary 16A72; Secondary 16A34
- DOI: https://doi.org/10.1090/S0002-9939-1985-0784162-4
- MathSciNet review: 784162