Gauss多项式环的理想和商环

The Ideal and Quotient Ring of Gauss Polynomial Ring

讨论了Gauss多项式环■[x,i]的理想和商环的性质.给出了Gauss多项式环的理想中次数最低元素的相伴元及一般表示,商环■[x,i]/〈u(x)+v(x)i〉中元素的一般表示,以及在特殊情况下Gauss多项式环理想和商环的形式和性质.

This paper mainly discusses some properties of the ideal and quotient ring of the Gauss polynomial ring■[x,i],gives the general form of the element with the minimum degree in the ideal of Gauss polynomial ring■[x,i]/〈u(x)+v(x)i〉,and the general form of elements in quotient ring of Gauss polynomial ring,and studies the structure and properties of ideal and quotient ring of Gauss polynomial ring Under special conditions.