2021•Siberian Mathematical JournalRequires access
Rings over Which Matrices Are Sums of Idempotent and $ q $-Potent Matrices
А. N. Abyzov, D. T. Tapkin
Open publisher page 8 citations
Abstract
We study the rings over which each square matrix is the sum of an idempotent matrix and a $ q $ -potent matrix. We also show that if $ F $ is a finite field not isomorphic to $ 𝔽_{3} $ and $ q>1 $ is odd then each square matrix over $ F $ is the sum of an idempotent matrix and a $ q $ -potent matrix if and only if $ q-1 $ is divisible by $ |F|-1 $ .