%0 Journal Article %T On the nil-clean matrix over a UFD %J Algebraic Structures and Their Applications %I Yazd University %Z 2382-9761 %A Hadjirezaei, Somayeh %A Karimzadeh, Somayeh %D 2015 %\ 11/01/2015 %V 2 %N 2 %P 49-55 %! On the nil-clean matrix over a UFD %K Rank of a matrix %K Idempotent matrix %K Nilpotent matrix %K Nil-clean matrix %K Strongly nil-clean matrix %R %X  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. %U https://as.yazd.ac.ir/article_803_7a98829c79d5ccc6521ac399e996e7bb.pdf