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

作　　者：张隆辉[1] 石化国[1] 张青山[1] ZHANG Long-hui;SHI Hua-guo;ZHANG Qing-shan(Sichuan Vocational and Technical College,Suining 629000,China)

机构地区：[1]四川职业技术学院,四川遂宁629000

出　　处：《数学的实践与认识》2020年第5期195-199,共5页Mathematics in Practice and Theory

基　　金：四川省教育厅自然科学重点项目(11ZA263,18ZA0434)。

摘　　要：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).

关 键 词：循环环 理想 素理想 极大理想 

分 类 号：O153.3[理学—数学]