這篇論文我們主要描述特徵數為2之質環上的Jordan同構Jordan導算。我們證明了在M_{n}(F),n>=3,上之Jordan同構一定是同構或反同構,假如n為奇數,n為偶數則不成立。
同時我們也刻劃出在M_{2}(GF(2))上的Jordan同構與Jordan導算。

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)).

Contents
1 Introduction 4
2 Preliminaries 4
2.1 Jordan isomorphisms on prime rings of
characteristic not 2 4
2.2 Jordan derivations on (semi)prime rings
of characteristic not 2 7
3 Main Results 9
3.1 Jordan isomorphisms on prime rings of
characteristic 2 9
3.2 Jordan derivations on prime rings of
characteristic 2 14

References
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