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 Sums of tripotent and nilpotent matrices Bull. Korean Math. Soc. 2018 Vol. 55, No. 3, 913-920 https://doi.org/10.4134/BKMS.b170384Published online May 31, 2018 Marjan Sheibani Abdolyousefi, Huanyin Chen Women's University of Semnan (Farzanegan), Hangzhou Normal University Abstract : Let $R$ be a 2-primal strongly 2-nil-clean ring. We prove that every square matrix over $R$ is the sum of a tripotent and a nilpotent matrices. The similar result for rings of bounded index is proved. We thereby provide a large class of rings over which every matrix is the sum of a tripotent and a nilpotent matrices. Keywords : tripotent matrix, nilpotent matrix, strongly 2-nil-clean ring, 2-prime ring MSC numbers : 16S34, 16U99, 16E50 Downloads: Full-text PDF