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 ...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.展开更多
基金Supported by Key Laboratory of Financial Mathematics of Fujian Province University(Putian University)(JR202203)the NSF of Anhui Province(2008085MA06).
文摘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.
