交换半环上矩阵的行列式秩  

Determinant Rank of Matrices over Commutative Semirings

作　　者：冯鑫 舒乾宇 FENG Xin;SHU Qianyu(School of Mathematical Sciences,Sichuan Normal University,Chengdu 610066,Sichuan)

机构地区：[1]四川师范大学数学科学学院,四川成都610066

出　　处：《四川师范大学学报（自然科学版）》2023年第4期477-487,共11页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11271132)。

摘　　要：在交换半环上首先研究矩阵的行列式秩与正、负复合矩阵的一些性质和关系,然后给出行列式秩与广义逆矩阵的一些相关结论,最后分别讨论行列式秩为1的矩阵其g-逆、群逆、M-P逆存在的充分必要条件.Over commutative semirings,we first study some properties and relations between the determinant rank of a matrix and its positive and negative composite matrices.Then we give some conclusions about the determinant rank of a matrix and its generalized inverse matrix.Finally some necessary and sufficient conditions for the existence of g-inverse,group inverse and M-P inverse of a ma-trix whose determinant rank is one are given.

关 键 词：交换半环 行列式秩 复合矩阵 广义逆矩阵 

分 类 号：O153[理学—数学]