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On strongly FP-injective accessibility and weakly FP-projective periodicity

  • Ilias Kaperonis
  • Konstantinos Golfis
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Abstract

Accessibility results are established for (Cartan-Eilenberg) strongly FP-injective complexes, by first proving the accessibility of Strongly FP-injective modules and then utilizing the pseudopullback theorem. We also prove that every acyclic complex of weakly FP-projective modules has weakly FP-projective cycles over left <ℵm-coherent rings for a non-negative integer m. This is achieved by introducing the cotorsion pairs (𝒞ℵmP−proj,𝒞ℵmP−inj), cogenerated by all ℵm-presentable weakly FP-projective modules, and proving that acyclic complexes of modules from the class 𝒞ℵmP−proj have weakly FP-projective cycles for every non-negative integer m.

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Cite

BibTeXRIS
BibTeX
@misc{kaperonis2026strongly,
  title = {{On strongly FP-injective accessibility and weakly FP-projective periodicity}},
  author = {Ilias Kaperonis and Konstantinos Golfis},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.38859},
  eprint = {2610.38859},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.38859},
}
RIS
TY  - UNPB
TI  - On strongly FP-injective accessibility and weakly FP-projective periodicity
AU  - Ilias Kaperonis
AU  - Konstantinos Golfis
PY  - 2026
DA  - 2026/10/28
PB  - arXiv
DO  - 10.48550/arxiv.2610.38859
UR  - https://arxiv.org/abs/2610.38859
AB  - Accessibility results are established for (Cartan-Eilenberg) strongly FP-injective complexes, by first proving the accessibility of Strongly FP-injective modules and then utilizing the pseudopullback theorem. We also prove that every acyclic complex of weakly FP-projective modules has weakly FP-projective cycles over left <ℵ_m-coherent rings for a non-negative integer m. This is achieved by introducing the cotorsion pairs (𝒞ℵ_mP−proj,𝒞ℵ_mP−inj), cogenerated by all ℵ_m-presentable weakly FP-projective modules, and proving that acyclic complexes of modules from the class 𝒞ℵ_mP−proj have weakly FP-projective cycles for every non-negative integer m.
ER  -