复形的#-内射包络的存在性

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英文篇名：The Existence of #-injective Envelopes of Complexes 作者：梁力 ; 杨刚 英文作者：Li LIANG;Gang YANG;School of Mathematics and Physics, Lanzhou Jiaotong University; 关键词：#-内射复形 ; 覆盖 ; 包络 ; 余挠对 英文关键词：#-injective complex;;cover;;envelope;;cotorsion pair 中文刊名：SXXB 英文刊名：Acta Mathematica Sinica(Chinese Series) 机构：兰州交通大学数理学院; 出版日期：2019-05-15 出版单位：数学学报(中文版) 年：2019 期：v.62 基金：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 语种：中文; 页：SXXB201903005 页数：6 CN：03 ISSN：11-2038/O1 分类号：41-46

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.
        Let ■ 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 ■ 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 ■-preenvelope, where ■ is the class of complete acyclic complexes of injective left R-modules.

引文

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