中文摘要：

假设d是无平方因子的整数,且d≠0,1,令K=Q（√d）,其中Q是有理数域.这时称K为一个二次域.对于某些二次域K,它的代数整数环Rd不是唯一分解整环.当d〈0时,称K为复二次域,此时K的代数整数环Rd是唯一分解整环当且仅当d=-1,-2,-3,-7,-11,-19,-43,-67,-163.令v为Rd中的素元,n是任意的正整数.当d=-1,-2,-3时,商环Rd/〈v^n〉的单位群结构已经被确定.该文获得了当d=-7时,Rd/〈v^n〉的单位群结构.

英文摘要：

For a square-free integer d other than 0 and 1,let K =Q（√d） , where Q is the set of rational numbers, then K is called a quadratic field. For several quadratic fields K =Q（√d） ,the ring Rd of integers of K is not a unique-factorization domain. For d〈0, there exists only a finite number of complex quadratic fields whose ring R d of integers, is a unique-factorization domain, namely d = 1,- 2,-3,--7,-11,-19,-43,-67,-163.Let v denote a prime element of Rd,n an arbitrary positive integer, the unit groups of R d/（v^n） have been determined for the cases d =-1,-2,-3. This paper completely determined the unit groups of Rd/（v^n） for the case d=-7.