循环准整环的构造  

Structure of Cyclic Near Domain

作　　者：张隆辉[1] 石化国[1] ZHANG Long-hui;SHI Hua-guo(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》2022年第5期226-229,共4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：研究了一类特殊循环环即循环准整环的构造,得到的主要结论有:1)所有的无限循环准整环就是M^(0)和<k)(k∈Z^(+)).2)设n(> 1)的标准分解式为n=p_(1)^(α_(1))p_(2)^(α_(2))…p_(s)^(α_(s)),ⅰ)若s=1,则n阶循环准整环共有α_(1)+1个,它们是dZ/ndZ,其中d=p_(1)^(β_(1)),0≤β_(1)≤α_(1);ⅱ)若s>1,则n阶循环准整环共有α_(1)α_(2)…α_(s)个,它们是dZ/ndZ,其中d=p_(1)^(β_(1))p_(2)^(β_(2))…p_(s)^(β_(s)),0 <β_(i)≤α_(i),i=1,2,…,s.This paper discuss structure of cyclic near domain,and get following results:(1)All infinite cyclic near domain are M~0 and (k∈Z^(+)).(2)Set the standard factorization of n(> 1) is n=p_(1)^(α_(1))_(2)^(α_(2))…p_(s)^(α_(s)),(ⅰ)If s=1,then the number of cyclic near dimain of order n is α_(1)+1,and all of them are dZ/ndZ,where d=p_(1)^(β_(1)),0≤β_(1)≤α_(1);(ⅱ)If s> 1,then the number of cyclic near dimain of order n is α_(1)α_(2)…α_(s),and all of them are dZ/ndZ,where d=p_(1)^(β_(1))p_(2)^(β_(2))…p_(s)^(β_(s)),0<β_(i)≤α_(i),i=1,2,…,s.

关 键 词：诣零根 循环环 准整环 循环准整环 

分 类 号：O153.3[理学—数学]