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

Su Hu*, Min Sha

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)369-380
Number of pages12
JournalPublicationes Mathematicae
Issue number3-4
Publication statusPublished - 2019


  • exceptional unit
  • finite commutative ring
  • character sum

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