关于环Zn中的幂等元问题

幂等元与本原幂等元在环中有非常重要的地位与作用。以数论为工具,通过解同余方程组,给出了环Zn中所有幂等元的计算公式,并讨论了环Zn中幂等元之间的一些关系式及利用幂等元对环Zn进行直和分解。通过幂等元与本原幂等元之间的关系,给出了环Zn中所有本原幂等元的计算公式。对于任何正整数n,只要知道n的素数分解式,就可以马上计算出环z n的所有幂等元及本原幂等元。

On the Problem about Idempotents in the Ring Zn

Idempotents and primitive idempotents have very important station in the ring.Using number theory,and through solving system of linear congruence equations,all the calculation formula of all idempotents in the ring Zn is proved.Furthermore,the paper discussed some relationships of idempotents and used idempotents to make a direct sum decomposition in the ring Zn..The calculation formulas of all primitive idempotents were given by using the relationships of idempotents and primitive idempotents.For any positive integer n,we can immediately calculate all idempotents and primitive idempotents in the ring Zn.as soon as the prime numbers decomposition of n is known.