Commutative local rings over which every upper-triangular matrix is the sum of an idempotent and a $q$-potent that commute

D. T. Tapkin

Kazan Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia

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.

Keywords: matrix ring, commutative local ring, idempotent, $q$-potent, Galois ring, nilpotent ideal.

UDC: 512.55

Received: 06.08.2024
Revised: 29.08.2024
Accepted: 26.09.2024

DOI: 10.26907/0021-3446-2026-1-72-84