%0 Journal Article %T On Weak Nil Clean Rings %A Zubayda M. Ibraheem %A Norihan N. Fadil %J Open Access Library Journal %V 9 %N 6 %P 1-7 %@ 2333-9721 %D 2022 %I Open Access Library %R 10.4236/oalib.1108812 %X If a ring R is called weak nil clean if every element in R can be expressed as the sum or difference of nilpotent element and idempotent, if further the idempotent element and nilpotent element commute the ring is called weak* nil clean. The purpose of this paper is to give some characterization and basic properties of weak nil clean rings. The main results of this work are: 1) Let R be a ring, then R is weak nil clean if and only if R/P(R) is weak nil clean; 2) In a commutative ring R, if x is weak nil clean element, then x^m is a weak nil clean element if (x-y)^m=ЁЦ_k-0^m (-1)^2k (_kⁿ)x^ky^m-k x,yЁЪR (2); 3) Let R be a ring with Idem(R) = {0,1}, then R is weak nil clean if and only if R is local ring and J(R) is Nil ideal. %K Clean Rings %K Nil Clean Rings %K Weak Nil Clean and Strongly Іа-Regular Rings %U http://www.oalib.com/paper/6774067