相对戈伦斯坦平面模块和福克斯比类及其模型结构

Pub Date : 2024-02-22 DOI:10.1142/s0219498825501944
Driss Bennis, Rachid El Maaouy, J. R. García Rozas, Luis Oyonarte
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引用次数: 0

摘要

我们为一个非必然半化模块引入了相对(强)扭转模块和相对戈伦斯坦扭转模块的概念,并证明存在一个唯一的遗传无性模型结构,其中共纤是具有相对戈伦斯坦平面内核的单形变,纤是具有相对扭转内核的属于巴斯类的外形变。在半双化模子的特殊情况下,我们研究了左(右)R 模子范畴中的无边模型结构的存在性,其中共纤是具有属于 Bass(Auslander)类的核(cokernel)的外变形(单变形)。我们还证明了相对戈伦斯坦平面模块类和巴斯类是弱 AB 上下文的一部分。
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Relative Gorenstein flat modules and Foxby classes and their model structures

We introduce the concepts of relative (strongly) cotorsion and relative Gorenstein cotorsion modules for a non-necessarily semidualizing module and prove that there exists a unique hereditary abelian model structure where the cofibrations are the monomorphisms with relative Gorenstein flat cokernel and the fibrations are the epimorphisms with relative cotorsion kernel belonging to the Bass class. In the particular case of a semidualizing module, we investigate the existence of abelian model structures on the category of left (right) R-modules where the cofibrations are the epimorphisms (monomorphisms) with kernel (cokernel) belonging to the Bass (Auslander) class. We also show that the class of relative Gorenstein flat modules and the Bass class are part of weak AB-contexts.

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