| 推出-拉回图上的覆盖性同态 |
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| 引用本文： | 周德旭.推出-拉回图上的覆盖性同态[J].数学研究及应用,2010,30(3):536-542. |
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| 作者姓名： | 周德旭 |
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| 作者单位： | 福建师范大学数学系, 福建 福州 350007 |
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| 基金项目： | 福建省自然科学基金(Grant No.2009J01003),福建师范大学青年骨干教师培养基金(Grant No.2008100209),福建省高校网络安全与密码重点实验室开放课题基金(Grant No.09A004). |
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| 摘 要： | In a pushout-pullback diagram,which consists of four morphisms f : A → B,g : A → C,α : C → D and β : B → D,we give some relations among the covers of these four modules.If kerf ∈ I(L ),then g : A → C is L -covering if and only if β : B → D is L -covering.If every module has an L -precover and kerf ∈ I(L ),then A and C have isomorphic L -precovers if and only if B and D have isomorphic L -precovers.
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| 关 键 词： | cover covering morphism pushout-pullback diagram. |
| 收稿时间： | 2008/3/23 0:00:00 |
| 修稿时间： | 1/5/2009 12:00:00 AM |
Covering Morphisms in a Pushout-Pullback Diagram |
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| De Xu ZHOU.Covering Morphisms in a Pushout-Pullback Diagram[J].Journal of Mathematical Research with Applications,2010,30(3):536-542. |
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| Authors: | De Xu ZHOU |
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| Institution: | Department of Mathematics, Fujian Normal University, Fujian 350007, P. R. China |
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| Abstract: | In a pushout-pullback diagram, which consists of four morphisms $f:A\rightarrow B$, $g:A\rightarrow C$, $\alpha:C\rightarrow D$ and $\beta:B\rightarrow D$, we give some relations among the covers of these four modules. If ker$f\in I({\mathscr{L}})$, then $g:A\rightarrow C$ is ${\mathscr{L}}$-covering if and only if $\beta:B\rightarrow D$ is ${\mathscr{L}}$-covering. If every module has an ${\mathscr{L}}$-precover and ker$f\in I({\mathscr{L}})$, then $A$ and $C$ have isomorphic ${\mathscr{L}}$-precovers if and only if $B$ and $D$ have isomorphic ${\mathscr{L}}$-precovers. |
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| Keywords: | cover covering morphism pushout-pullback diagram |
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