• The Pure and Applied Mathematics
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• v.21 no.4
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• pp.237-246
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• 2014

Let M be a prime ${\Gamma}$-ring and let d be a derivation of M. If there exists a fixed integer n such that $(d(x){\alpha})^nd(x)=0$ for all $x{\in}M$ and ${\alpha}{\in}{\Gamma}$, then we prove that d(x) = 0 for all $x{\in}M$. This result can be extended to semiprime ${\Gamma}$-rings.

• Journal of the Korean Mathematical Society
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• v.46 no.4
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• pp.675-689
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• 2009

As a sequel to the papers [2, 3], we will complete our identification of the groups of units of the finite local rings $\mathbb{Z}_4$[X]/($X^k$ + 2t(X), $2X^{\gamma}$) which is the most general type of finite local rings with a single nilpotent generator over $\mathbb{Z}_4$.