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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

We study Gorenstein flat objects in the category Rep(Q,R) of representations of a left rooted quiver Q with values in Mod(R), the category of all left R-modules, where R is an arbitrary associative ring. We show that a representation X in Rep(Q,R) is Gorenstein flat if and only if for each vertex i the canonical homomorphism φiX:a:jiX(j)X(i) is injective, and the left R-modules X(i) and CokerφiX are Gorenstein flat. As an application, we obtain a Gorenstein flat model structure on Rep(Q,R) 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 代表(,电阻)具有值的左根箭袋Q的表示模组(电阻),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代表(,电阻)Gorenstein 是平坦的当且仅当每个顶点i的规范同态φ一世X一种j一世X(j)X(一世)是单射的,左边的R模块X(一世)焦化器φ一世X是戈伦斯坦平坦的。作为一个应用,我们获得了一个 Gorenstein 平面模型结构代表(,电阻) 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。

更新日期:2021-06-09
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