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Finitistic injective dimension exceeding finitistic projective dimension for a commutative ring

  • Liang Chen
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Abstract

We construct a commutative ring whose big finitistic projective dimension is $1$ and whose big finitistic injective dimension is $2$. The example contradicts the comparison suggested by Bass for commutative rings.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026finitistic,
  title = {{Finitistic injective dimension exceeding finitistic projective dimension for a commutative ring}},
  author = {Liang Chen},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.18254},
  eprint = {2609.18254},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.18254},
}
RIS
TY  - UNPB
TI  - Finitistic injective dimension exceeding finitistic projective dimension for a commutative ring
AU  - Liang Chen
PY  - 2026
DA  - 2026/09/16
PB  - arXiv
DO  - 10.48550/arxiv.2609.18254
UR  - https://arxiv.org/abs/2609.18254
AB  - We construct a commutative ring whose big finitistic projective dimension is $1$ and whose big finitistic injective dimension is $2$. The example contradicts the comparison suggested by Bass for commutative rings.
ER  -