【摘 要】
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It is proved that for matrices A,B in the n by n upper triangular matrix ring Tn(R) over a domain R,if AB is nonzero and central in Tn(R) then AB =BA.The n by n
【机 构】
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Department of Mathematics, Yanbian University, Yanji, Jilin 133002, China;Department of Mathematics,
论文部分内容阅读
It is proved that for matrices A,B in the n by n upper triangular matrix ring Tn(R) over a domain R,if AB is nonzero and central in Tn(R) then AB =BA.The n by n full matrix rings over right Noetherian domains are also shown to have this property.In this article we treat a ring property that is a generalization of this result,and a ring with such a property is said to be weakly reversible-over-center.The class of weakly reversible-over-center rings contains both full matrix rings over right Noetherian domains and upper triangular matrix rings over domains.The structure of various sorts of weakly reversible-over-center rings is studied in relation to the questions raised in the process naturally.We also consider the connection between the property of being weakly reversible-over-center and the related ring properties.
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