Addition Of A Full Matrix Algebra Idempotent Preserving Mapping

Suppose R is an idempotence-diagonalizable ring. Let n and m be two arbitrary positive integers with n ≥ 3. We denote by M_n(R) the ring of all n × n matrices over R. Let ＜J_n(R)＞ be the additive subgroup of M_n(R) generated additively by all idempotent matrices. Let U = ＜J_n(R)＞ or M_n(R). We describe the additive preservers of idempotence from U to M_m(R) when 2 is a unit of R. Thereby, we also characterize the Jordan (respectively, ring and ring anti-) homomorphisms from M_n(R) to M_m(R) when 2 is a unit of R, the additive preservers of tripotence from U to M_m(R) when 2 and 3 are units of R and the additive preservers of inverses ( respectively, Drazin, group , {1}-, {2}- and {1,2}-) inverses from M_n(R) to M_m(R) when R is any idempotence-diagonalizable ring with 2,3 ∈R~*.