| Abel范畴中态射乘积诱导的短正合列及其应用 |
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| 引用本文： | 李桃生.Abel范畴中态射乘积诱导的短正合列及其应用[J].数学学报,1995,38(6):732-737. |
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| 作者姓名： | 李桃生 |
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| 作者单位： | 华中师范大学数学系 |
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| 摘 要： | 本文给出了Ａｂｅｌ范畴中态射乘积αβγ诱导的短正合列的立体交换图。其中共有７个３×３平面，３０条线。每一条线（两端的零对象省略）都是一个短正合列．这些短正合列用到ｐ－除环上的矩阵，可以导出一系列矩阵秩的恒等式，它不仅推广了域上矩阵秩的结果，还能得到一些新的关系式．
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| 关 键 词： | Abel范畴，态射，短正合列，p－除环，矩阵的秩 |
| 收稿时间： | 1993-10-5 |
Theshort Exact Seqliences Induced by Product of Morphism and Their Applications in Abel Categories |
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| Li Taosheng.Theshort Exact Seqliences Induced by Product of Morphism and Their Applications in Abel Categories[J].Acta Mathematica Sinica,1995,38(6):732-737. |
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| Authors: | Li Taosheng |
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| Institution: | Li Taosheng( Department of Mathematics,Central China Normal University,Wuhan 430070,China) |
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| Abstract: | In the paper we give solid commulative diagram of short exact sequences induced by product αβγof morphisms. There are seven 3 × 3 planes,30 lines in the commutative diagram,every line (zero object of both ends be omitted)is a short exact sequence。These short exact sequences can induce a series of identity on the rank of matrices over p-division ring.Our resuhts not only generalize some results of rank of matrices over field,also can obtain some new dependence relations and formulas. |
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| Keywords: | Abel category morphism short exact sequence p-division ring rank of matrix |
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