首页 | 本学科首页   官方微博 | 高级检索  
     检索      

集合上非一一变换构成的群及其在矩阵代数中的表现
引用本文:朱一心,海进科.集合上非一一变换构成的群及其在矩阵代数中的表现[J].首都师范大学学报(自然科学版),2003,24(2):5-14.
作者姓名:朱一心  海进科
作者单位:1. 首都师范大学数学系,北京,100037
2. 青岛大学数学系,青岛,266071
基金项目:国家自然科学基金项目资助 ( 10 2 710 81)
摘    要:发现任意集合A上一个由非一一变换关于变换乘法构成的群与A的某个子集上一个变换群的同构;证明A上一个非一一变换f能出现在一个由A上变换构成的乘法群中当且仅当f(A)上的限制Resy^λ(λ)f为f(A)上一一变换.然后将结论用到短阵代数中,给出数域F上n级短阵M满足秩M=秩M^2的充要条件.

关 键 词:集合  非一一变换  变换群  乘法群  矩阵代数  变换乘法

Groups Generated by Non-bijective Transformations on a Setand Their Representations in the Matrix Algebra
Zhu Yixin.Groups Generated by Non-bijective Transformations on a Setand Their Representations in the Matrix Algebra[J].Journal of Capital Normal University(Natural Science Edition),2003,24(2):5-14.
Authors:Zhu Yixin
Abstract:We assert here that a group generated by non\|bijective transformations on a set A is isomorphic to a permutation group on a subset of A,and prove that a non bijective transformation f on A occurs in a group consisting of non\|bijective transformations if and only if that the restriction to f(A) of f is bijective.Also with these statements we give the necessary and sufficient conditions for a matrix M on a field F satisfying that the ranks of M and M\+2 are the same.
Keywords:transformation  bijective  permutation group  matrix  rank    
本文献已被 CNKI 维普 万方数据 等数据库收录!
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号