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.
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).
