| 集合上非一一变换构成的群及其在矩阵代数中的表现 |
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| 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 |
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| 作者姓名： | 朱一心 海进科 |
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| 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 |
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| 基金项目： | 国家自然科学基金项目资助 ( 10 2 710 81) |
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| 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．
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| 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 |
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| 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 |
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| Authors: | Zhu Yixin |
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| 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. |
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| Keywords: | transformation bijective permutation group matrix rank. |
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