Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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GROUP RINGS SATISFYING NIL CLEAN PROPERTY

  • Received : 2019.01.16
  • Accepted : 2019.07.17
  • Published : 2020.01.31
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Abstract

In 2013, Diesl defined a nil clean ring as a ring of which all elements can be expressed as the sum of an idempotent and a nilpotent. Furthermore, in 2017, Y. Zhou, S. Sahinkaya, G. Tang studied nil clean group rings, finding both necessary condition and sufficient condition for a group ring to be a nil clean ring. We have proposed a necessary and sufficient condition for a group ring to be a uniquely nil clean ring. Additionally, we provided theorems for general nil clean group rings, and some examples of trivial-center groups of which group ring is not nil clean over any strongly nil clean rings.

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References

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