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唯一分解整环上的矩阵分解问题

李冬梅1,刘金旺1,关剑成2   

  1. 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
  • 出版日期:2017-10-25 发布日期:2017-12-14

李冬梅,刘金旺,关剑成. 唯一分解整环上的矩阵分解问题[J]. 系统科学与数学, 2017, 37(10): 2042-2051.

LI Dongmei, LIU Jinwang,GUAN Jiancheng. Problems of Matrix Factorization over Unique Factorization Domain[J]. Journal of Systems Science and Mathematical Sciences, 2017, 37(10): 2042-2051.

Problems of Matrix Factorization over Unique Factorization Domain

LI Dongmei1 ,LIU Jinwang1 ,GUAN Jiancheng2   

  1. 1. School of Mathematics and Computing Sciences, Hunan University of Science and Technology, Xiangtan 411201; 2. School of Mathematics and Computing Sciences, Hunan Normal University, Changsha 410081
  • Online:2017-10-25 Published:2017-12-14

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.

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