报告题目 (Title)：Nil clean group rings over metacyclic groups
中文标题：在metacyclic群上的Nil clean群环
报告人 (Speaker)： 李元林 教授 （加拿大布鲁克大学）
报告时间 (Time)：2025年6月12日（周四）15：30
报告地点 (Place)：校本部GJ303
邀请人(Inviter)：黄红娣
报告摘要：A ring is nil clean if each of its elements is the sum of an idempotent and a nilpotent. Previously in [J. Cui, Y. Li and H. Wang. On nil clean group rings, Commun. Algebra 49(2) (2021) 790-796], the nil clean group rings over dihedral groups and generalized quaternion groups were completely determined. In this paper, we investigate group rings RG over more general metacyclic groups G. We provide a new criterion for a general nil clean group ring based on the upper central series of G consisting of 2-groups,
and whether the group ring over its respective factor group is nil clean. We also determine values of m and n (as a prime power) in order for RG to be nil clean, and verify whether their corresponding group rings are indeed nil clean.