| 刘仲奎,李方.关于局部Noether模(英文)[J].数学研究及应用,2000,20(4):491~497 |
| 关于局部Noether模(英文) |
| On Locally Noetherian Modules |
| 投稿时间：1997-10-20 |
| DOI：10.3770/j.issn:1000-341X.2000.04.003 |
| 中文关键词: |
| 英文关键词:locally noetherian module finitely cogenerated module X-modu |
| 基金项目: |
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| 摘要点击次数: 2088 |
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| 中文摘要: |
| 本文证明了如下结果：左 Ｒ－模 Ｍ是局部 Ｎｏｅｔｈｅｒ模当且仅当σ［Ｍ］中的任意Ｍ－内射左Ｒ－模的直和是一个有限余生成左Ｒ－模和一个拟连续（或连续，直内射）左Ｒ－模的直和． |
| 英文摘要: |
| This paper is devoted to give some characterizations of locally noetherian modules by finitely cogenerated modules and generalized injective modules. It is proved that a left R-module M is locally noetherian if and only if every direct sum of M-injective left R-modules in σ[M] is the direct sum of a finitely cogenerated left R-module and a quasi-continuous (or, continuous, or, direct-injective, etc,) left R-module. |
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