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arXiv · 1612.04539

On the additive and multiplicative structures of the exceptional units in finite commutative rings

Su Hu·Min Sha
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Abstract

Let $R$ be a commutative ring with identity. A unit $u$ of $R$ is called exceptional if $1-u$ is also a unit. When $R$ is a finite commutative ring, we determine the additive and multiplicative structures of its exceptional units; and then as an application we find a necessary and sufficient condition under which $R$ is generated by its exceptional units.

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Su Hu, Min Sha. 2016-12-14. On the additive and multiplicative structures of the exceptional units in finite commutative rings. https://arxiv.org/abs/1612.04539

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