Reveals criteria for commutative local rings where upper-triangular matrices are sums of commuting idempotent and q-potent elements.
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 F_pᵏ[x]/ xʳ , necessary and sufficient criteria are provided.
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D. T. Tapkin (2026) studied this question.
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