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Derivations in prime near-rings


Author: Xue Kuan Wang
Journal: Proc. Amer. Math. Soc. 121 (1994), 361-366
MSC: Primary 16Y30; Secondary 16W25
DOI: https://doi.org/10.1090/S0002-9939-1994-1181177-7
MathSciNet review: 1181177
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Abstract: Let N be a prime near-ring with center Z. The purpose of this paper is to study derivations on N. We show two main results: (1) Let N be 2-torsion-free, and let $ {D_1}$ and $ {D_2}$ be derivations on N such that $ {D_1}{D_2}$ is also a derivation. Then either $ {D_1}$ or $ {D_2}$ is zero if and only if $ [{D_1}(x),{D_2}(y)] = 0$ for all $ x,y \in N$. (2) Let n be an integer $ \geq 1$, N be n!-torsion-free, and D a derivation with $ {D^n}(N) = \{ 0\} $. Then $ D(Z) = \{ 0\} $.


References [Enhancements On Off] (What's this?)

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DOI: https://doi.org/10.1090/S0002-9939-1994-1181177-7
Article copyright: © Copyright 1994 American Mathematical Society

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