The theory of finitely generated relative (co)tilting modules has been established in the 1980s by Auslander and Solberg, and infinitely generated relative tilting modules have recently been studied by many authors in the context of Gorenstein homological algebra. In this work, we build on the theory of infinitely generated Gorenstein tilting modules by developing “Gorenstein tilting approximations” and employing these approximations to study Gorenstein tilting classes and their associated relative cotorsion pairs. As applications of our results, we discuss the problem of existence of complements to partial Gorenstein tilting modules as well as some connections between Gorenstein tilting modules and finitistic dimension conjectures.

Auslander 和 Solberg 在 1980 年代建立了有限生成相对（共）倾斜模的理论，最近许多作者在 Gorenstein 同调代数的背景下研究了无限生成相对倾斜模。在这项工作中，我们通过开发“Gorenstein 倾斜近似”并利用这些近似来研究 Gorenstein 倾斜类及其相关的相对 cotorsion 对，以无限生成的 Gorenstein 倾斜模块理论为基础。作为我们结果的应用，我们讨论了部分 Gorenstein 倾斜模块的补体的存在问题以及 Gorenstein 倾斜模块和有限维数猜想之间的一些联系。