凝聚环是一类十分重要的环，许多经典的环都可以视为凝聚环的特例。在环论以及相对同调代数中，很多重要的结果都基于环的凝聚性，同时也产生了一些悬而未决的问题。自20世纪80年代以来，导出范畴和三角范畴得以广泛应用，这是现阶段同调代数的特征。近年来，与三角范畴有关的同调代数理论被成功地应用于环与代数的表示理论，其中就包括在凝聚环上的应用。本项目拟围绕与凝聚环有关的环类展开研究，充分发展当前同调代数中与三角范畴有关的新方法和新工具（包括挠理论、余挠理论、倾斜理论、silting理论、t-结构、余t-结构、粘合等）以及环与模的广义內射性、模的覆盖与包络、自同态环、环的各种扩张等传统工具，并应用于环与代数的结构与表示，争取在一些与凝聚环相关的热点问题上取得新的进展。

Coherent rings are very important since many classical rings can be considered as a special case of such rings. Moreover, in ring theory and relative homological algebra, many important results are based on the coherence of rings, and many open problems are posed thereby. Since 1980s, as a significant feature of homological algebra, derived categories and triangulated categories have been widely applied to many academic fields. In recent years, the theory homological algebra related to triangulated categories has been successfully applied to the representation theory of rings and algebras, including the application to coherent rings. This project intends to focus on coherent rings and some rings related to them based on a full development of new methods and tools in homological algebra in terms of triangulated categories (including torsion theory, cotorsion theory, silting theory, t-structure, co-t-structure, recollement, etc.) and some traditional tools such as generalized injectivity of rings and modules, covers and envelopes, endomorphism rings, extensions of rings. The results will be applied to the study on structures and representations of rings and algebras so that some new progress will be made in some related issues on coherent rings.