在本篇論文裡，我們回顧Posner的兩個定理，並討論它們的推廣。第一定理敘述，在特徵數不為二的質環上，如果兩個導算的合成是一個導算，那個這兩個導算的其中之一必定為零。第二定理描述，如果d是在質環R上的一個非零導算，使得在R上的所有元素x滿足交換子xd(x)-d(x)x屬於R的中心，那麼R是可交換的。

In this thesis, we review two well-known theorems of E. C. Posner and their generalizations. The first of the two asserts that if the product of two derivations on a prime ring of characteristic not two is a derivation, then one of the derivations must be zero, and the second says that if d is a nonzero derivation on a prime ring R such that the commutator xd(x)−d(x)x is in the center of R for all x in R, then R is commutative.

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