| 分次版本的Enochs定理 |
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| 引用本文： | 吴小英,王芳贵.分次版本的Enochs定理[J].山东大学学报(理学版),2018,53(10):22-26. |
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| 作者姓名： | 吴小英 王芳贵 |
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| 作者单位： | 四川师范大学数学学院, 四川 成都 610068 |
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| 基金项目： | 国家自然科学基金资助项目(11671283) |
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| 摘 要： | 证明了分次版本的Enochs定理: 设A是有限生成分次R-模B的分次子模, 若对任何FP-gr-内射 R-模E, 分次同态f:A→E恒能扩张到B, 则A是有限生成的。 由此得到有限生成分次R-模M是有限表现的当且仅当对任何FP-gr-内射模E, 都有EXT1R(M,E)=0。
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| 关 键 词： | 有限表现模 FP-内射模 FP-gr-内射模 分次超有限表现模 |
| 收稿时间： | 2018-03-22 |
Graded version of Enochs theorem |
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| WU Xiao-ying,WANG Fang-gui.Graded version of Enochs theorem[J].Journal of Shandong University,2018,53(10):22-26. |
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| Authors: | WU Xiao-ying WANG Fang-gui |
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| Institution: | College of Mathematics, Sichuan Normal University, Chengdu 610068, Sichuan, China |
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| Abstract: | It is shown that graded version of Enochs theorem is proved. Let B be a finitely generated graded R-module and let A be a graded submodule of B. If every graded homomorphsim f: A→E can be extended to B for any FP-gr-injective R-module E, then A is finitely generated. It follows that a finitely generated graded R-module M is finitely presented if and only if EXT1R(M,E)=0 for any FP-gr-injective module E. |
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| Keywords: | FP-injective module graded super finitely presented module FP-gr-injective module finitely presented module |
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