由一个加群构造的一类交换环

A class of rings constructed by an abelian group

由一个加群G=(〈x〉 ,〈y〉) ,此处mx≠ 0 ,my≠ 0 ,对任意非零整数m ,构造出一类交换环Rm,m=1 ,2 ,3,… ,使得Rm 与Rn(m ≠n)不同构 ,且对任何m与n ,Rm 有无穷多个同构于Rn 的子环 .

Constructed a class of commutative rings from an abelian group G=(〈x〉,〈y〉), where mx≠0,my≠0 for any integer m≠0. In this class, there are infinite number of commutative rings R m,m=1,2,3,…, such that (1)R mR n for m≠n; (2)for any m and n, there are infinite number of subrings of R m , which are isomorphic to R n.