本論文探討Jordan與Lie 結構在質環Prime Ring上主要特質，並整理簡述相關的古典理論。內容主要是探討質環上 Jordan和 Lie的同構---homomorphism與導算---Derivation的相關型態與結果。

We will discuss some properties of Jordan and Lie homomorphisms and derivations on prime rings. We first give some definitions and then we show some classic results .

1. INTRODUCTION AND PRELIMINARIES……3
1.1 Introduction……3
1.2 Preliminaries……4
2. JORDAN AND LIE HOMOMORPHISMS……6
2.1 Jordan and Lie structure……6
2.2 Jordan Homomorphisms……7
2.3 Lie Homomorphisms……10
3. JORDAN AND LIE DERIVATIONS……15
3.1 Jordan Derivations……15
3.2 Lie Derivations……17
References……20

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