复形的Cartan-Eilenberg Gorenstein AC-同调维数  

Cartan-Eilenberg Gorenstein AC-cohomology dimension of complexes

作　　者：张丽英 杨刚[1] ZHANG Li-ying;YANG Gang(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,Gansu,China)

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070

出　　处：《山东大学学报（理学版）》2020年第4期77-84,共8页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11761045);甘肃省自然科学基金资助项目(17JR5RA091,18JR3RA113);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：研究了Cartan-Eilenberg Gorenstein AC-内射(投射)复形的若干等价刻画。证明了复形G是Cartan-Eilenberg Gorenstein AC-内射(投射)复形当且仅当G具有Cartan-Eilenberg强完全内射(L完全投射)分解。并且研究了复形的Cartan-Eilenberg Gorenstein AC-内射(投射)维数。Some equivalent characterizations of Cartan-Eilenberg Gorenstein AC-injective(projective) complexes are studied. It is proved that a complex G is Cartan-Eilenberg Gorenstein injective(projective) if and only if G has a Cartan-Eilenberg strongly complete injective(L complete projective) resolution. Also, the Cartan-Eilenberg Gorenstein AC-injective(projective) dimension of complexes is studied.

关 键 词：绝对clean模(复形) GORENSTEIN AC-内射(投射)模 Cartan-Eilenberg GORENSTEIN AC-内射(投射)复形 

分 类 号：O154.2[理学—数学]