We prove that Jordan elementary surjective maps on rings are automatically additive. Elementary operators were originally introduced by Brešar and Šerml ([1]). In the last decade, elementary maps on operator algebras as well as on rings attracted more and more attentions. It is very interesting that elementary maps and Jordan elementary maps on some algebras and rings are automatically additive...

In this paper, we characterize a class of additive maps on Hilbert C∗-modules which maps a ”rank one” adjointable operators to another rank one operators.