| 有限生成模与内射模的子模闭 |
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| 引用本文： | 甘志雄. 有限生成模与内射模的子模闭[J]. 长沙理工大学学报(社会科学版), 1988, 0(4) |
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| 作者姓名： | 甘志雄 |
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| 作者单位： | 长沙水电师院数学系 |
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| 摘 要： | 本文提出有限生成模与内射模的子模闭的充要条件,即:每一有限生成R—模的子模仍为有限生成模的充要条件是:R的每一左理想均为有限生成R—模。每一内射R—模的子模仍为内射模的充要条件是:R的每一左理想均为内射R—模。
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| 关 键 词： | 有限生成模 Noether模 内射模 |
SUBMODULE CLOSURE OF FINITELY GENERATEI) MODULE AND INJECTIVE MODULE |
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| Gang Zhixong Mathematics Department. SUBMODULE CLOSURE OF FINITELY GENERATEI) MODULE AND INJECTIVE MODULE[J]. Journal of Changsha University of Science & Technology, 1988, 0(4) |
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| Authors: | Gang Zhixong Mathematics Department |
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| Affiliation: | Gang Zhixong Mathematics Department |
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| Abstract: | This paper discusses some necessary and sufficicnt conditions aboutsubmodule closure of finitely generated module and injective module. Each ofthem is as follows. Every submodule of finitely generated R-module is also finitely generatedif and only if every left ideal of R is a finitely generated R-module. Every submodule of injective R-module is also injective if and only ifevery left ideal of R is an injective R-module. |
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| Keywords: | finitely generated R-module Noetherian R-module injective R-module |
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