Group rings satisfying nil clean property
Commun. Korean Math. Soc. 2020 Vol. 35, No. 1, 117-124
https://doi.org/10.4134/CKMS.c190018
Published online January 31, 2020
Sehoon Eo, Seungjoo Hwang, Woongyeong Yeo
Korea Science Academy of KAIST; Korea Science Academy of KAIST; Korea Science Academy of KAIST
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.
Keywords : Idempotent, nilpotent, nil clean, uniquely nil clean, group ring
MSC numbers : Primary 16S34, 16U99
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