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Abstract <p>We study commutative local rings over which every upper-triangular matrix is the sum of an idempotent and a <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(q\)</EquationSource> <!--RusMath2670006Tapkin-m1--> </InlineEquation>-potent that commute. For Galois rings and rings of the form <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({{\mathbb{F}}_{{{{p}^{k}}}}}[x{\text{]/}}\langle {{x}^{r}}\rangle \)</EquationSource> <!--RusMath2670006Tapkin-m2--> </InlineEquation>, necessary and sufficient criteria are provided.</p>

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Commutative Local Rings over Which Every Upper-Triangular Matrix Is the Sum of an Idempotent and a q-Potent That Commute

  • 期刊论文

  • 发表日期：

    2026年1月1日

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  • D. T. Tapkin

摘要

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 \({{\mathbb{F}}_{{{{p}^{k}}}}}[x{\text{]/}}\langle {{x}^{r}}\rangle \) , necessary and sufficient criteria are provided.