主理想整环上的线性方程组的解

本文讨论了主理想整环上的一次方程组,给出了求齐次方程组的基础解系的方法;一组解能构成或者能生成基础解系的充要条件;非齐次方程组有解的充要条件和求解的方法。特别是在欧氏整环上,上面的各种判别和求解都可以通过矩阵的初等变换实现。文中的结论用于解整数环上的线性方程组十分简便实用。

SOLUTION OF SYSTEM OF LINEAR EQUATIONS ON THE PRINCIPAL IDEAL DOMAIN

This thesis discusses the system of linear equations on the principals ideal domain, gives the method of finding fundamental system of solutions of homogeneous equations-the necessary and sufficient conditions of a group solutions can form, or can be expanded into or can generate the fundamental system of solutions,it qives tKe necessary and sufficient conditions of nonhomogeneous equations have solution and the method of solvig them,particularly on the Euclidean integral domain, these identifyings and solvings can be realized through the elementary operation of matrix. Solving the linear equations on the integral ring with these method in this thesis are highly simple, convenient and practical.