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Gorenstein flat representations of left rooted quivers
Journal of Algebra ( IF 0.9 ) Pub Date : 2021-06-02 , DOI: 10.1016/j.jalgebra.2021.05.008 Zhenxing Di , Sergio Estrada , Li Liang , Sinem Odabaşı
中文翻译:
左根箭袋的 Gorenstein 平面表示
更新日期:2021-06-09
Journal of Algebra ( IF 0.9 ) Pub Date : 2021-06-02 , DOI: 10.1016/j.jalgebra.2021.05.008 Zhenxing Di , Sergio Estrada , Li Liang , Sinem Odabaşı
We study Gorenstein flat objects in the category of representations of a left rooted quiver Q with values in , the category of all left R-modules, where R is an arbitrary associative ring. We show that a representation X in is Gorenstein flat if and only if for each vertex i the canonical homomorphism is injective, and the left R-modules and are Gorenstein flat. As an application, we obtain a Gorenstein flat model structure on in which we give explicit descriptions of the subcategories of trivial, cofibrant and fibrant objects.
中文翻译:
左根箭袋的 Gorenstein 平面表示
我们研究该类别中的 Gorenstein 平面物体 具有值的左根箭袋Q的表示,所有左R模的范畴,其中R是任意结合环。我们证明了一个表示X在Gorenstein 是平坦的当且仅当每个顶点i的规范同态是单射的,左边的R模块 和 是戈伦斯坦平坦的。作为一个应用,我们获得了一个 Gorenstein 平面模型结构 其中我们对琐碎的、共纤维的和纤维的物体的子类别进行了明确的描述。