Journal of Guangxi Normal University(Natural Science Edition) ›› 2016, Vol. 34 ›› Issue (1): 72-77.doi: 10.16088/j.issn.1001-6600.2016.01.011

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Strong 2-sum Property of Local Rings and Their Extensions

TANG Gaohua, WU Yansheng, ZHANG Hengbin, LI Yu   

  1. School of Mathematics and Statistics,Guangxi Teachers Education University, Nanning Guangxi 530023,China
  • Received:2015-08-23 Published:2018-09-14

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Abstract: An element of a ring R is called to have the strong 2-sum property if it is a sum of two units that commute with each other. And a ring R is called a strong 2-sum ring if every element of R has the strong 2-sum property. Local ring is a very important class of rings. Local rings and their extensions are very important in the research of ring theory,module theory and homological algebra. In this article, a characterization of a local ring to be a strong 2-sum ring is given. Then, the strong 2-sum property of local rings and their power series extension,trivial extension and matrix extension are studied.

Key words: 2-good ring, strong 2-sum ring, local ring, ring extension

CLC Number: 

  • O153.3
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