相对Gorenstein平坦维数与模型结构  

Relative Gorenstein flat dimension and model structures

作　　者：赵仁育 王久玉 ZHAO Ren-yu;WANG Jiu-yu(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,Gansu,China)

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《西北师范大学学报(自然科学版)》2025年第2期52-58,共7页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(11861055)。

摘　　要：设R是环,n是非负整数,GF_(B)^(≤n)(R)和PGF_(B)^(≤n)(R)分别表示GorensteinB-平坦维数不超过n的左R-模类和投射余可解GorensteinB-平坦维数不超过n的左R-模类,其中B是一个半可定义的右R-模类.给出了GF_(B)^(≤n)(R)和PGF_(B)^(≤n)(R)的刻画,利用这两个模类构造了两个遗传阿贝尔模型结构的链,并证明了这些模型结构的同伦范畴均与PGF_(B)(R)的稳定范畴三角等价.Let R be a ring,n be a non-negative integer,GF_(B)^(≤n)(R)and PGF_(B)^(≤n)(R)be the classes of left R-modules with Gorenstein B-flat dimension at most n and the classes of left R-modules with projectively coresolved Gorenstein B-flat dimension at most n,respectively,where B is a class of semi-definable right R-modules.Some characterizations of GF_(B)^(≤n)(R)and PGF_(B)^(≤n)(R)are given respectively,and established two chains of hereditary Abelian model structures in terms of these two classes of left R-modules.It is showed that the homotopy categories of these model structures are all triangle equivalent to the stable category of PGF_(B)(R).

关 键 词：Gorenstein B-平坦维数 投射余可解Gorenstein B-平坦维数 余挠对 阿贝尔模型结构 

分 类 号：O153.3[理学—数学]