Gauss整数环的主理想及其商环研究

Research the Principal Ideal and Quotient Ring of Gaussian Integral Domain

研究了Gauss整数环商环中元素的个数问题,并用一种新的初等方法解决了以下猜想:Gauss整数环的商环(Z[i]/(n+mi))元素个数是m2+n2.

The definition and some properties of the quotient ring, the unit and the simple element of Gauss integral ring are discussed, element numbers of the quotient ring of Gauss integral ring is researched, and proves one of the two eonjectuires of Arch. with a new and elementary method. In light of the Gaussian integral domain, the num-ber of elements of its ring of quotients is m^2＋n^2.