欧氏环上矩阵的广义初等变换及应用  

Generalized Elementary Transformation of Matrix on Euclidad Ring and Its Applications

作　　者：张景晓[1] 

机构地区：[1]德州学院数学系,山东德州253023

出　　处：《重庆理工大学学报（自然科学）》2010年第8期100-103,共4页Journal of Chongqing University of Technology：Natural Science

基　　金：国家"十一五"质量工程项目(FIOBO70335-A2);德州学院精品课程基金资助项目(JP-A07010)

摘　　要：建立了欧氏环上矩阵的广义初等变换的概念,证明了欧式环上矩阵的广义初等变换不改变矩阵的最大公因子,并将这一结论应用于求整数的最大公因数,求多个一元多项式的最大公因式以及求Guass整数环Z[i]中数的最大公因数。In this paper,the concepts of generalized elementary transformation of matrix on Euclidad ring are established,and that the greatest common factor of matrix on Euclidad ring is unchanged for generalized elementary transformation of matrix is proved.Then this result is applied to solve the greatest common divisor of integers,the greatest common divisor of polynomial and the greatest common factor of elements in Z[i].

关 键 词：欧式环 广义初等变换 最大公因子 

分 类 号：O153.3[理学—数学]