循环准整环的构造

Structure of Cyclic Near Domain

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.