实二次域K=Q((5n)^(1/2))的整数环O_K

The Ring O_K of Integers of the Real Quadratic Number Field K=Q((5n)^(1/2))

用简单的证明方法推出实二次域K=Q((5n)^(1/2))(其中n为正整数,5n无平方因子)的整数环OK只有在n=24t+1(t∈Z)的时候才有可能是主理想整环,其他情况下,二次域K=((5n)^(1/2))的整数环OK一定不是主理想整环。

It is deduced in this paper that ring Ok of integers of the real quadratic number field K = Q（√5n） ,Sn squarefree, n 〉 0, may be a principal ideal domain when n is 24t ＋ 1 （ t ∈ Z ^＋ ）, otherwise, the ring OK must not be a principal ideal domain.