Determining unit groups and K1 of finite rings
Abstract
We consider the computational problem of determining the unit group of a finite ring, by which we mean the computation of a finite presentation together with an algorithm to express units as words in the generators. We show that the problem is equivalent to the number theoretic problems of factoring integers and solving discrete logarithms in finite fields. A similar equivalence is shown for the problem of determining the abelianization of the unit group or the first K -group of finite rings.
Fields of Study & Subjects
Finite Group Theory Research
Rings
Modules
and Algebras
graph theory and CDMA systems
Publication details
- Journal / source
- Journal of Algebra
- Volume
- 693
- Pages
- 510–530
- Publication date
- 20 January 2026
- Language
- EN