@article { author = {Hadjirezaei, Somayeh and Karimzadeh, Somayeh}, title = {On the nil-clean matrix over a UFD}, journal = {Algebraic Structures and Their Applications}, volume = {2}, number = {2}, pages = {49-55}, year = {2015}, publisher = {Yazd University}, issn = {2382-9761}, eissn = {2423-3447}, doi = {}, abstract = { 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.}, keywords = {Rank of a matrix,Idempotent matrix,Nilpotent matrix,Nil-clean matrix,Strongly nil-clean matrix}, url = {https://as.yazd.ac.ir/article_803.html}, eprint = {https://as.yazd.ac.ir/article_803_7a98829c79d5ccc6521ac399e996e7bb.pdf} }