蛇引理在长正合列定理证明中的应用

Application of the Snake Lemma to the Proof of the Long Exact Sequence Theorem

研究了蛇引理在长正合列定理证明中的应用;首先利用给定的两个复形来定义两个新复形,然后利用这两个新复形构造出一个复形正合列,进而构造出一个满足蛇引理条件的交换图,最后利用蛇引理给出长正合列定理的一个简单的证明。

In this paper,we study the application of the snake lemma to the proof of the long exact sequence theorem, firstly, we define two new complexes from the given two complexes; secondly, we construct an exact sequence of complexes by using the two new complexes and a commutative diagram which satisfies the conditions of snake lemma ; and finally we give a simple proof for the long exact sequence theorem by using the snake lemma.