| 关于所有子模是纯子模的平坦模 |
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| 引用本文： | 杨曼丽.关于所有子模是纯子模的平坦模[J].数学研究,2006,39(1):32-35. |
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| 作者姓名： | 杨曼丽 |
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| 作者单位： | 浙江丽水学院数学系,浙江,丽水,323000 |
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| 基金项目： | ACKN0WLEDGEMENTS The author would like to thank Professor Huanyin Chen for his helpful comments. |
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| 摘 要： | 引进了一新模类-完全平坦模(每一个商模平坦).并得到了:令M是平坦左R-模,RM是完全平坦模当且仅当RM的所有子模是纯的当且仅当每一个右R-模A是M-平坦的.同时本文用完全平坦模刻画了V.N.正则环.
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| 关 键 词： | 商模 完全平坦模 纯子模 V.N.正则环 |
| 收稿时间： | 2004-09-21 |
| 修稿时间： | 2004年9月21日 |
Flat Module of Which Every Submodule is Pure |
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| Yang Manli.Flat Module of Which Every Submodule is Pure[J].Journal of Mathematical Study,2006,39(1):32-35. |
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| Authors: | Yang Manli |
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| Abstract: | In this paper, we introduce the completely flat module class. A letf R-module M is called completely flat module if every factor module of M is flat. Let M is a flat left R-module, we get that _R M is a completely flat module iff all submodules of _R M are pure or erery right R-module A is M-flat. It is proven that a ring R is V.N. regular iff every factor module of the injective R-module is flat. |
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| Keywords: | Factor module Completely flat Pure submodule V N regular ring |
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