强Gorenstein AC-内射复形及维数  

Strongly Gorenstein AC-injective complexes and dimensions

作　　者：汪鑫 卢博[1] WANG Xin;LU Bo(College of Mathematics and Computer Science,Northwest Minzu University,Lanzhou 730030,China)

机构地区：[1]西北民族大学数学与计算机科学学院,甘肃兰州730030

出　　处：《浙江大学学报（理学版）》2024年第4期426-433,共8页Journal of Zhejiang University（Science Edition）

基　　金：中央高校基本科研业务经费(31920230173);国家自然科学基金资助项目(12061061);甘肃省第一批陇原青年英才项目。

摘　　要：设n为任意整数,引入并研究了强Gorenstein AC-内射复形,证明了复形X是强Gorenstein AC-内射复形当且仅当Xn是Gorenstein AC-内射模,且对任意的DG-绝对clean复形A,复形同态f:A→X是零伦的。特别地,若X为有界正合复形,则X的强Gorenstein AC-内射性等价于模Z_n(X)的Gorenstein AC-内射性,也等价于模Xn的Gorenstein AC-内射性。此外,引入并研究了复形的强Gorenstein AC-内射维数。Let n be any integer.The notion of strongly Gorenstein AC-injective complexes is introduced and studied.It is proven that a complex X is strongly Gorenstein AC-injective if and only if each Xn is a Gorenstein AC-injective module and any homomorphism f:A→X is null homotopic whenever A is a DG-absolutely clean complex.In particular,if a complex X is bounded and exact,then the strongly Gorenstein AC-injectivity of a complex X is equivalent to the Gorenstein AC-injectivity of the module Zn(X),and is also equivalent to the Gorenstein ACinjectivity of the module Xn.In addition,the notion of strongly Gorenstein AC-injective dimension of complexes is introduced and studied.

关 键 词：强Gorenstein AC-内射复形 Gorenstein AC-内射模 DG-绝对clean复形 维数 

分 类 号：O154.2[理学—数学]