Abstract
Let $R$ be a finite commutative ring. In this paper, we find the number of representations of a fixed member of $R$ to be the sum of $k$ units in $R$, and the sum of $k$ non-units, and as a sum of a unit and a non-unit. We prove that, if $\Z _2$ is not a quotient of $R$, then every $r\in R$ can be written as a sum of $k$ units, for each integer $k > 1$.
Citation
Dariush Kiani. Mohsen Mollahajiaghaei. "On the addition of units and non-units in finite commutative rings." Rocky Mountain J. Math. 45 (6) 1887 - 1896, 2015. https://doi.org/10.1216/RMJ-2015-45-6-1887
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