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

2016/12/14 by Su Hu, Min Sha, Hu, Su +1
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1612.04539

openalex publication_date 2016/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• On the addition of units and nonunits mod m

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