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
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