| 拟离散模的消去性 |
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| 引用本文： | 张伟民,陈治中.拟离散模的消去性[J].北京交通大学学报(自然科学版),1997(2). |
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| 作者姓名： | 张伟民 陈治中 |
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| 作者单位： | 北方交通大学数学系 |
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| 摘 要： | 对拟离散的消去性作了讨论，得到如下主要结果：（１）模Ｍ有提升性当且仅当Ｍ的每一个余闭子模是Ｍ的直和项；（２）拟离散模的子模的任何两个余闭包是超视的，因而是同构的；（３）拟离散模有消去性当且仅当其每一个为直和项的空子模有消去性；（４）在有消去性的拟离散模中，若其两个子模的商模同构，则这两个子模的余闭包同构．
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| 关 键 词： | 拟连续模 拟离散模 余闭子模 余闭包 消去性 |
The Cancellation Property of Quasi Discrete Modules |
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| Zhang Weimin\ Chen Zhizhong.The Cancellation Property of Quasi Discrete Modules[J].JOURNAL OF BEIJING JIAOTONG UNIVERSITY,1997(2). |
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| Authors: | Zhang Weimin\ Chen Zhizhong |
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| Abstract: | In this paper,we make some discussions in the central problem of the cancellation property of quasi discrete modules and obtain the following main results:(1) M has the lifting property if and only if any co closed submodule is a summand of M ; (2)Any two co closures of a submodule of quasi discrete module M are superspective, and hence isomorphic; (3)A quasi discrtet module M has cancellation property if and only if any empty submodule N of M is a summand of M which has cancellation property; (4)In a quasi discrete module M with cancellation property, if factor module of any two submodules of M are isomorphic, then the co closures of the submodules are isomprphic. |
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| Keywords: | quasi continuous modules\ quasi discrete modules co closed submodules\ co closures\ cancellation property |
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