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PreprintarXiv licencearXiv

Quasi-projective dimensions over homological ring epimorphisms

  • Weiheng Xia
  • Xiaolei Zhang
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Abstract

In this paper, we study quasi-projective dimensions of modules over rings connected by homological ring epimorphisms. We establish several inequalities relating the quasi-projective dimensions over the source and target rings. As applications, we investigate the quasi-global dimension of triangular matrix rings and provide examples showing that the class of modules with finite quasi-projective dimension does not satisfy the 2-out-of-3 property in general.

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Cite

BibTeXRIS
BibTeX
@misc{xia2026quasiprojective,
  title = {{Quasi-projective dimensions over homological ring epimorphisms}},
  author = {Weiheng Xia and Xiaolei Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.41614},
  eprint = {2610.41614},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.41614},
}
RIS
TY  - UNPB
TI  - Quasi-projective dimensions over homological ring epimorphisms
AU  - Weiheng Xia
AU  - Xiaolei Zhang
PY  - 2026
DA  - 2026/10/30
PB  - arXiv
DO  - 10.48550/arxiv.2610.41614
UR  - https://arxiv.org/abs/2610.41614
AB  - In this paper, we study quasi-projective dimensions of modules over rings connected by homological ring epimorphisms. We establish several inequalities relating the quasi-projective dimensions over the source and target rings. As applications, we investigate the quasi-global dimension of triangular matrix rings and provide examples showing that the class of modules with finite quasi-projective dimension does not satisfy the 2-out-of-3 property in general.
ER  -