MATRICES OVER A REDUCED RING AS SUMS OF THREE TRIPOTENTS  

约化环上可分解为三个三幂等矩阵之和的矩阵

作　　者：HUANG Tao CUI Jian ZENG Yue-di 黄涛;崔建;曾月迪(安徽师范大学数学与统计学院,安徽芜湖241002;金融数学福建省高校重点实验室(莆田学院),福建莆田351100)

机构地区：[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

出　　处：《数学杂志》2024年第5期406-412,共7页Journal of Mathematics

基　　金：Supported by Key Laboratory of Financial Mathematics of Fujian Province University(Putian University)(JR202203);the NSF of Anhui Province(2008085MA06).

摘　　要：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 M_(n)(R)is a sum of three tripotents if and only if R■Zp with p=2,3,5 or 7.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,M_(n)(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：Tripotent companion matrix reduced ring matrix ring 

分 类 号：O153.3[理学—数学]