| Covering Morphisms in a Pushout-Pullback Diagram |
| Received:March 23, 2008 Revised:January 05, 2009 |
| Key Words:
cover covering morphism pushout-pullback diagram.
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| Fund Project:Supported by the Natural Science Foundation of Fujian Province (Grant No.2009J01003), the Foundation of Fujian Normal University (Grant No.2008100209) and partially by the Open Funds of Key Lab of Fujian Province University Network Security and Cryptology (Grant No.09A004). |
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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. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2010.03.018 |
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