标题： 诺特世界中的特征倾斜模与Ringel对偶性 显示英文标题

标题： Characteristic tilting modules and Ringel duality in the Noetherian world

摘要： 分裂拟旗余代数在交换诺特环上的Ringel对偶性的基础得到了加强。 提供了关于包含所有标准模的最小解析子范畴的几种描述和性质。 特别是，给定两个分裂拟旗余代数$A$和$B$，我们证明了任何关于包含所有标准模的最小解析子范畴在$A$和包含所有标准模的最小解析子范畴在$B$之间的精确等价可以提升为一个保持拟旗余代数结构的Morita等价，该等价在$A$和$B$之间。 显示英文摘要

摘要： The foundations of Ringel duality for split quasi-hereditary algebras over commutative Noetherian rings are strengthened. Several descriptions and properties of the smallest resolving subcategory containing all standard modules over split quasi-hereditary algebras over commutative Noetherian rings are provided. In particular, given two split quasi-hereditary algebras $A$ and $B$, we prove that any exact equivalence between the smallest resolving subcategory containing all standard modules over $A$ and the smallest resolving subcategory containing all standard modules over $B$ lifts to a Morita equivalence between $A$ and $B$ which preserves the quasi-hereditary structure.