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
推出-拉回图上的覆盖性同态
Covering Morphisms in a Pushout-Pullback Diagram
投稿时间:2008-03-23  最后修改时间:2009-01-05
DOI:10.3770/j.issn:1000-341X.2010.03.018
中文关键词:  覆盖  覆盖性同态  推出-拉回图.
英文关键词:cover  covering morphism  pushout-pullback diagram.
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).
作者单位
周德旭 福建师范大学数学系, 福建 福州 350007 
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中文摘要:
      在由四个同态$f:A\rightarrow B$, $g:A\rightarrow C$, $\alpha:C\rightarrow D$ 以及 $\beta:B\rightarrow D$构成的推出-拉回图上, 我们给出了这四个模的覆盖之间的关系.若ker$f\in I({\mathscr{L}})$,则$g:A\rightarrow C$为${\mathscr{L}}$-覆盖性同态当且仅当$\beta:B\rightarrow D$为${\mathscr{L}}$-覆盖性同态. 若每个模都有${\mathscr{L}}$-预覆盖且ker$f\in I({\mathscr{L}})$, 则$A$和$C$有同构的${\mathscr{L}}$-预覆盖当且仅当$B$和$D$也有同构的${\mathscr{L}}$-预覆盖.
英文摘要:
      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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