Additive preservers of idempotence and Jordan homorphisms between rings of square matrices

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 〈(R)〉 be the additive subgroup of M _n (R) generated additively by all idempotent matrices. Let = 〈(R)〉 or M _n (R). We describe the additive preservers of idempotence from 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. This work is supported in part by the Chinese Natural Science Foundation under Grant No. 10671026 and the Postdoctoral Fund of Heilongjiang Province