For a Quillen exact category \({\mathcal {C}}\) endowed with two exact structures \({\mathcal {D}}\) and \({\mathcal {E}}\) such that \({\mathcal {E}}\subseteq {\mathcal {D}}\), an object X of \({\mathcal {C}}\) is called \({\mathcal {E}}\)-divisible (respectively \({\mathcal {E}}\)-flat) if every short exact sequence from \({\mathcal {D}}\) starting (respectively ending) with X belongs to \({\mathcal {E}}\). We continue our study of relatively divisible and relatively flat objects in Quillen exact categories with applications to finitely accessible additive categories and module categories. We derive consequences for exact structures generated by the simple modules and the modules with zero Jacobson radical.

对于Quillen精确类别\（{\ mathcal {C}} \\）赋予两个精确结构\（{\ mathcal {D}} \）和\（{\ mathcal {E}} \\）使得\（{ mathcal {E}} \ subseteq {\ mathcal {d}} \），对象X的\（{\ mathcal {C}} \）被称为\（{\ mathcal {E}} \） -divisible（分别\ （{\ mathcal {E}} \）- flat）如果\（{\ mathcal {D}} \）中每个以X开头（分别结束）的简短序列都属于\（{\ mathcal {E}} \\。我们将继续研究Quillen精确类别中相对可分割和相对平坦的对象，并将其应用于有限可访问的加性类别和模块类别。我们推导出简单模块和具有零Jacobson根的模块生成的精确结构的结果。