发表机构
College of Mathematics and Statistics, Northwest Normal University; Gansu Provincial Research Center for Basic Disciplines of Mathematics and Statistics（西北师范大学数学与统计学院; 甘肃省数学与统计学基础学科研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在逗号范畴、平凡环扩张、Morita环及形式三角矩阵环中构造左（右）n-余挠对，研究其遗传性质，改进并提升了相关已知结果。
AI 中文摘要
本文主要研究两类阿贝尔范畴中的n-余挠对。首先，通过改进同调群之间的若干同构，并结合逗号范畴中的若干对象类，我们在逗号范畴中构造了左（右）n-余挠对。其次，基于平凡环扩张上已知的同调公式，我们研究了这类环上满足特定条件的若干模类，并通过这些模类在平凡环扩张上建立了左（右）n-余挠对，随后直接给出了具有零双模同态的Morita环上的相应结论。我们在上述两种情形下都研究了左（右）n-余挠对的遗传性质。最后，将在逗号范畴和平凡环扩张上得到的主要结果应用于形式三角矩阵环，同时通过这些应用发现，已知结果中的相关条件得到了改进，且已知结果的结论得到了提升。
英文摘要
In this paper, we mainly investigate $n$-cotorsion pairs in two types of abelian categories. Firstly, we construct left (right) $n$-cotorsion pairs in comma categories by improving some isomorphisms between homology groups and combining some classes of objects in comma categories. Secondly, based on known homological formulas over trivial ring extensions, we study some classes of modules satisfying certain conditions over such rings, and we establish left (right) $n$-cotorsion pairs over trivial ring extensions through these classes. Then corresponding conclusions over Morita rings with zero bimodule homomorphisms are directly presented. The hereditary property of left (right) $n$-cotorsion pairs is investigated in both cases. Finally, we apply main results obtained in comma categories and over trivial ring extensions to formal triangular matrix rings. At the same time, via these applications, we found that relevant conditions in known results have been improved and the known results have been elevated.
