有限局部环上方阵的几种新型拓展广义逆  

New Extended Generalized Inverses of N-order Matrices over Finite Local Ring

作　　者：吴炎 WU Yan(School of Science,Hainan Tropical Ocean University,Sanya Hainan 572022,China;Editorial Department of the Journal,Hainan Tropical Ocean University,Sanya Hainan 572022,China)

机构地区：[1]海南热带海洋学院理学院 [2]海南热带海洋学院学报编辑部,海南三亚572022

出　　处：《海南热带海洋学院学报》2021年第5期49-55,98,共8页Journal of Hainan Tropical Ocean University

基　　金：海南省自然科学基金项目(117150)。

摘　　要：设R=Z/p^(k)Z是有限局部环,p是一个奇素数,k为大于1的正整数,A是R上给定的可相似对角化的n阶矩阵。基于所给新型拓展广义逆的定义,并利用了环R上矩阵方法和组合方法,讨论了矩阵A的新型拓展广义逆,得到了矩阵A的几种新型拓展广义逆存在的充要条件,以及这几类拓展广义逆的一些计数结果。Let R=Z/p^(k)Z be a finite local ring,with p as the odd prime,k as the positive integer greater than 1,A as the similarly diagonalizable n-order matrices over R.Based on the new extended definition of generalized inverse,by making use of the matrix method and combination method over the ring,new types of the extended generalized inverse matrices of matrix A was discussed.Consequently,the necessary and sufficient conditions as well as some counting results of the several new existence of extended generalized inverses were obtained.

关 键 词：可相似对角化矩阵 有限局部环 拓展广义逆矩阵 计数定理 

分 类 号：O151.21[理学—数学]