Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ON COMMUTATIVITY OF NILPOTENT ELEMENTS AT ZERO

  • Abdul-Jabbar, Abdullah M. (Department of Mathematics University of Salahaddin-Erbil) ;
  • Ahmed, Chenar Abdul Kareem (Department of Mathematics University of Zakho) ;
  • Kwak, Tai Keun (Department of Mathematics Daejin University) ;
  • Lee, Yang (Institute of Basic Science Daejin University)
  • Received : 2017.01.02
  • Accepted : 2017.05.19
  • Published : 2017.10.31
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Abstract

The reversible property of rings was initially introduced by Habeb and plays a role in noncommutative ring theory. In this note we study the reversible ring property on nilpotent elements, introducing the concept of commutativity of nilpotent elements at zero (simply, a CNZ ring) as a generalization of reversible rings. We first find the CNZ property of 2 by 2 full matrix rings over fields, which provides a basis for studying the structure of CNZ rings. We next observe various kinds of CNZ rings including ordinary ring extensions.

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References

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