Ring in which every element is sum of two ۶-potent elements

‎In this paper, we prove the following results‎. ‎Every element of a ring R is a sum of two commuting ۶-potent elements if and only if R is isomorphic to R_۱\times R_۲\times R_۳‎, ‎where R_۱ is isomorphic to a subdirect product of Z_۲'s‎, ‎R_۲ is isomorphic to a subdirect product of Z_۳'s and R_۳ is isomorphic to a subdirect product of Z_{۱۱}'s‎. ‎Also, if every element of a ring R is the sum of two ۶-potent and one nilpotent all commute with each other, then R is isomorphic to R_۱\times R_۲\times R_۳‎, ‎where J(R_۱) is nil and R_۱/J(R_۱) is a subdirect product of rings isomorphic to either of the rings Z_۲,F_۴,M_۲(F_۲) and M_۲(F_۴)‎ , ‎a^{۸۱}-a is nilpotent for every a\in R_۲‎ , ‎J(R_۳) is nil and R_۳/J(R_۳) is a subdirect product of Z_{۱۱}'s‎.

کلیدواژه ها:

۴-potents ، ۶-potents ، Chinese Remainder Theorem