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2015 On the addition of units and non-units in finite commutative rings
Dariush Kiani, Mohsen Mollahajiaghaei
Rocky Mountain J. Math. 45(6): 1887-1896 (2015). DOI: 10.1216/RMJ-2015-45-6-1887

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 $k > 1$.

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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

Information

Published: 2015
First available in Project Euclid: 14 March 2016

zbMATH: 1332.05088
MathSciNet: MR3473160
Digital Object Identifier: 10.1216/RMJ-2015-45-6-1887

Subjects:
Primary: 05C25, 05C50

Rights: Copyright © 2015 Rocky Mountain Mathematics Consortium

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Vol.45 • No. 6 • 2015
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