| 摘要: |
| 本文研究了每个元素均可表示为三个互相交换的三幂等元之和的约化环,给出了整环上任意n阶矩阵均可表示为三个三幂等矩阵之和的判定条件, 证明了对于整环 R, Mn(R) 中任意矩阵可分解为三个三幂等矩阵之和当且仅当R≌Zp, 其中p=2, 3, 5或7. |
| 关键词: 三幂等元 友矩阵 约化环 矩阵环 |
| DOI： |
| 分类号:O153.3 |
| 基金项目: |
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| MATRICES OVER A REDUCED RING AS SUMS OF THREE TRIPOTENTS |
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HUANG Tao1, CUI Jian1,2, ZENG Yue-di2
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1.School of Mathematics and Statistics, Anhui Normal University, Wuhu 241002, China;2.Key Laboratory of Financial Mathematics (Putian University), Fujian Province University, Putian 351100, China
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| Abstract: |
| In this paper, we study reduced rings in which every element is a sum of three tripotents that commute, and determine the integral domains over which every n×n matrix is a sum of three tripotents. It is proved that for an integral domain R,, every matrix in Mn(R) is a sum of three tripotents if and only if R≌Zp with p=2, 3, 5 or 7. |
| Key words: Tripotent companion matrix reduced ring matrix ring |
