唯一分解整环上的矩阵分解问题  

Problems of Matrix Factorization over Unique Factorization Domain

作　　者：李冬梅[1] 刘金旺[1] 关剑成 LI Dongmei;LIU Jinwang;GUAN Jiancheng(School of Mathematics and Computing Sciences, Hunan University of Science and Technology, Xiangtan 411201;School of Mathematics and Computing Sciences, Hunan No~nal University, Changsha 410081)

机构地区：[1]湖南科技大学数学与计算科学学院,湘潭411201 [2]湖南师范大学数学与计算科学学院,长沙410081

出　　处：《系统科学与数学》2017年第10期2042-2051,共10页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(11501192);湖南省自然科学基金(2017JJ3084);湖南省教育厅项目(15B082;17C0644)资助课题

摘　　要：主要讨论唯一分解整环上矩阵的子式素分解和因子素分解问题,得到该环上判别任意矩阵是否具有子式素分解的充分必要条件,并对行满秩矩阵给出其关于其正则因子是否存在因子素分解的判定条件.We investigate the problems of minor prime factorization and factor prime factorization for matrices over UFD. The sufficient and necessary condition for the existence of minor prime factorization or factor prime factorization for matrices over UFD are obtained. For matrices of full row rank, we present conditions for determining the existence of their factor prime factorizations with respect to their regular factors.

关 键 词：矩阵分解 子式素分解 因子素分解 唯一分解整环 

分 类 号：O151.21[理学—数学]