复形的#-内射包络的存在性  

The Existence of #-injective Envelopes of Complexes

作　　者：梁力[1] 杨刚[1] Li LIANG;Gang YANG(School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, P. R. China)

机构地区：[1]兰州交通大学数理学院,兰州730070

出　　处：《数学学报（中文版）》2019年第3期391-396,共6页Acta Mathematica Sinica：Chinese Series

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

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.

关 键 词：#-内射复形 覆盖 包络 余挠对 

分 类 号：O154.2[理学—数学]