Commutative local rings over which every upper-triangular matrix is the sum of an idempotent and a q-potent that commute
Abstract
We study commutative local rings over which every upper-triangular matrix is the sum of an idempotent and a $q$-potent that commute. For Galois rings and rings of the form $\mathbb{F}_{p^{k}}[x]/\langle x^{r} \rangle$, necessary and sufficient criterion are provided.
Fields of Study & Subjects
Rings
Modules
and Algebras
Matrix Theory and Algorithms
Advanced Topics in Algebra
Publication details
- Journal / source
- Russian Mathematics
- Issue
- 1
- Pages
- 72–84
- Publication date
- 12 February 2026
- Language
- EN