[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.c190018

GROUP RINGS SATISFYING NIL CLEAN PROPERTY

Eo, Sehoon (Korea Science Academy of KAIST)
Hwang, Seungjoo (Korea Science Academy of KAIST)
Yeo, Woongyeong (Korea Science Academy of KAIST)

Publication Information

Communications of the Korean Mathematical Society / v.35, no.1, 2020 , pp. 117-124 More about this Journal

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;

Citations & Related Records

Reference

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