On the nil-clean matrix over a UFD

Document Type : Research Paper


Vali-e-Asr University of Rafsanjan


 In this paper we characterize all $2\times 2$ idempotent and nilpotent matrices over an integral domain and then we characterize all $2\times 2$ strongly nil-clean matrices over a PID. Also, we determine when a $2\times 2$ matrix  over a UFD is nil-clean.


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