Every Jordan isomorphism of triangular n¡Ñn matrices over F with characteristic 2 is either a isomorphism or a antiisomorphism while n is 2. But it is not true for n ¡Ù 3.

In this thesis, we describe the Jordan isomorphisms and Jordan derivations on prime rings of characteristic 2. We prove that every Jordan isomorphism of M_{n}(F),n >= 3 is either an isomorphism or an antiisomorphism if n is odd, and it is not true if n is even. We also describe the Jordan isomorphisms and Jordan derivations on M_{2}(GF(2)).