Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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SINGULAR CLEAN RINGS

  • Amini, Afshin (Department of Mathematics College of Sciences Shiraz University) ;
  • Amini, Babak (Department of Mathematics College of Sciences Shiraz University) ;
  • Nejadzadeh, Afsaneh (Department of Mathematics College of Sciences Shiraz University) ;
  • Sharif, Habib (Department of Mathematics College of Sciences Shiraz University)
  • Received : 2017.09.24
  • Accepted : 2018.02.21
  • Published : 2018.09.01
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Abstract

In this paper, we define right singular clean rings as rings in which every element can be written as a sum of a right singular element and an idempotent. Several properties of these rings are investigated. It is shown that for a ring R, being singular clean is not left-right symmetric. Also the relations between (nil) clean rings and right singular clean rings are considered. Some examples of right singular clean rings have been constructed by a given one. Finally, uniquely right singular clean rings and weakly right singular clean rings are also studied.

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References

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