| 复形的#-内射包络的存在性 |
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| 引用本文： | 梁力,杨刚. 复形的#-内射包络的存在性[J]. 数学学报, 2019, 62(3): 391-396 |
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| 作者姓名： | 梁力 杨刚 |
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| 作者单位： | 兰州交通大学数理学院 兰州 730070 |
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| 基金项目： | 国家自然科学基金资助项目（11761045,11561039）;甘肃省自然科学基金资助项目（18JR3RA113,17JR5RA091）;兰州交通大学"百名青年优秀人才培养计划"基金资助项目 |
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| 摘 要： | 令■表示所有#-内射左R-模复形构成的类(即内射左R-模的复形构成的类).本文证明了在左诺特环R上■是完备的内射余挠对.特别地,我们得到每个左R-模复形都有#-内射包络.作为应用,证明了在左诺特环R上,每个左R-模复形都有特殊■-预包络,其中■是所有内射左R-模的完全零调复形构成的类.
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| 关 键 词： | #-内射复形 覆盖 包络 余挠对 |
The Existence of #-injective Envelopes of Complexes |
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| Li LIANG,Gang YANG. The Existence of #-injective Envelopes of Complexes[J]. Acta Mathematica Sinica, 2019, 62(3): 391-396 |
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| Authors: | Li LIANG Gang YANG |
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| Affiliation: | School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, P. R. China |
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| Abstract: | Let dwI denote the class of #-injective complexes of left R-modules (i.e., complexes of injective left R-modules). We prove that over left noetherian rings R, the pair (⊥(dwI), dwI) is a perfect injective cotorsion pair. In particular, we get that every complex of left R-modules has a #-injective envelope. As an application, we prove that over left noetherian rings R, every complex of left R-modules has a special Etac (I)-preenvelope, where Etac (I) is the class of complete acyclic complexes of injective left R-modules. |
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| Keywords: | #-injective complex cover envelope cotorsion pair |
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