Czechoslovak Mathematical Journal, first online, pp. 1-9


Unit nil-clean and singular clean group rings

Rajendra Kumar Sharma, Amit B. Singh

Received September 3, 2024.   Published online March 5, 2025.

Abstract:  We study the unit nil-cleanness of group rings when $R$ is commutative or arbitrary. Furthermore, we investigate some properties of singular clean group rings. A necessary and sufficient condition for the group ring $RG$ to be singular clean is provided.
Keywords:  unit nil-clean ring; clean ring; $p$-group; locally finite group; singular clean ring; UU ring; nil-clean ring
Classification MSC:  16U99, 16S34

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Affiliations:   Rajendra Kumar Sharma, Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110 016, India, e-mail: rksharmaiitd@gmail.com; Amit B. Singh (corresponding author), Jamia Hamdard University, Mehrauli - Badarpur Rd, Block D, Hamdard Nagar, New Delhi 110 062, India, e-mail: amit.bhooshan84@gmail.com


 
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