关于循环环的理想、素理想和极大理想

About Ideal、Prime Ideal and Maxianal Ideal of Cyclical Rings

研究了循环环R=的理想、素理想和极大理想的个数和结构,得到了如下结论:1)理想:(1)若|R|=∞,则R共有无穷多个理想:;(2)若|R|=n,设n的正因数个数为T(n),则R共有T(n)个理想:.2)素理想:(1)若|R|=∞,设a^2=ka(k≥0),①当k=0时,R的素理想只有R;②当k>0时,R的素理想共有无穷多个,它们是:{0}、R及;(2)若|R|=n>1,设a^2=ka,0≤k.3)极大理想:(1)若|R|=∞,则R有无限多个极大理想,它们是;(2)若|R|=n>1,设n的互不相同的素因数个数为ψ(n),则R共有ψ(n)个极大理想:(pa|p是n的素因数).

Let R=be a cyclical ring.This paper studid the structure and number of R’s ideal、prime ideal and maximal ideal,and get following resualts:1)Ideal:(1)If|R|=∞,then there are infinite ideanls of R:;(2)If|R|=n,then there are T(n)(The number of positive factor of n)ideals of R:.2)Prime ideal:(1)If|R|=∞,Let a^2=ka(k≥0),①When k=0,Rhas only one prime ideal R itself;②when k>0,there are infinite prime ideal of R:{0}、R and;2)If|R|=n>1,let a^2=ka,0≤k;2)If|R|=n>1,letψ(n)be the number positive prime factor of n,then there areψ(n)maximal ideals of R:(pa|p is a positive prime factor of n).