On right n-C_2 rings

The concept of right n-C2 rings was introduced in this note.The following result were shown:(1)R was right n-C2 rings if and only if there existed a positive integer n,for every a∈R,and if r(an)=r(e),where e2=e∈R,then e∈Ran.(2) If R is right n-C2 rings,then Zr(R)J(R).(3) For a ring R the following are equivalent:(i) R is n-regular rings(ii) R is right n-C2 rings and right n-Gpp rings.