关于交换环上矩阵嵌入可逆矩阵的一些条件  

Some Conditions for a Matrix to be Embeddable in an Invertible Matrix over a Commutative Ring

作　　者：郭小芳 谭宜家[1] GUO Xiaofang;TAN Yijia(School of Mathematics and Computer Science,Fuzhou University,Fuzhou 350108,China)

机构地区：[1]福州大学数学与计算机科学学院,福建福州350108

出　　处：《吉林化工学院学报》2020年第11期91-93,共3页Journal of Jilin Institute of Chemical Technology

基　　金：国家自然科学基金面上项目(11971111);福建省自然科学基金面上项目(2016J01012)。

摘　　要：给出了交换环上一个矩阵可嵌入到可逆矩阵的一个必要条件和一个充分条件,进而证明了主理想整环上一个n阶矩阵可嵌入到一个n+1阶可逆矩阵的充要条件是这个矩阵的伴随矩阵的元素是互素的.部分结果推广了整数环上的结论.A necessary condition and a sufficient condition for a matrix to be embeddable in an invertible matrix over a commutative ring are given.Furthermore,it is proved that a necessary and sufficient condition for a matrix of order nto be embeddable in an invertible matrix of order n+1 over a principal ideal domain is that the elements in the adjoint matrix of this matrix are relatively prime.Partial results obtained in this paper generalize the corresponding results for the ring of integers.

关 键 词：矩阵 可逆矩阵 嵌入 交换环 主理想整环 

分 类 号：O151.21[理学—数学]