基于齐次线性方程组的解在环上的应用  

Application of Solution Based on Homogeneous Linear Equations on Ring

作　　者：庞峰 PANG Feng(Shanxi Police College,Taiyuan 030401,China)

机构地区：[1]山西警察学院,山西太原030401

出　　处：《太原师范学院学报（自然科学版）》2020年第3期17-24,共8页Journal of Taiyuan Normal University:Natural Science Edition

基　　金：山西警察学院2020院级教学改革创新项目重点课题(YJ202012)。

摘　　要：环是代数中最古老最丰富的分支之一,是抽象代数的基础.文章利用抽象代数的基本知识及方法,在环的范围上对高等代数中齐次线性方程组的解的结构和性质进行了研究.结果表明,当方程组的系数矩阵是满秩矩阵时,齐次线性方程只有零解,而剩余类环Z m,不仅有零解,也存在非零解.The ring is one of the oldest and richest branches in algebra,and it is the basis of abstract algebra.In this paper,the basic knowledge and methods of abstract algebra are used to study the structure and properties of solutions of homogeneous linear equations in higher algebra in the scope of rings.The results show that when the coefficient matrix of the system of equations is a full-rank matrix,homogeneous linear equations have only zero solutions,and the remaining rings Z_m have not only zero solutions but also non-zero solutions.

关 键 词：实数域 环 齐次线性方程组 

分 类 号：O13[理学—数学]