Construction of n-cotorsion pairs in some abelian categories

@misc{chen2026construction,
  title = {{Construction of $n$-cotorsion pairs in some abelian categories}},
  author = {Wenjing Chen and Junjie Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.03299},
  eprint = {2609.03299},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.03299},
}

TY  - UNPB
TI  - Construction of n-cotorsion pairs in some abelian categories
AU  - Wenjing Chen
AU  - Junjie Zhang
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2609.03299
UR  - https://arxiv.org/abs/2609.03299
AB  - 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.
ER  -