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A strongly compact cardinal yields a left and right coherent ring with $\mathcal{PGF}(R)\subsetneq\mathcal{GP}(R)$ — arXiv:2608.17748

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.17748
License (as archived): CC0-1.0
Archived: 2026-10-18T15:16:38.208Z
SHA-256 of the archived text: 04b4af44124c928bb35ff7666dbb45d334c12c5828ebd171ab1b871c5f21af97
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How to cite

A strongly compact cardinal yields a left and right coherent ring with $\mathcal{PGF}(R)\subsetneq\mathcal{GP}(R)$ — arXiv:2608.17748 — arXiv (en), https://arxiv.org/abs/2608.17748 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_161a0eebdada (Metraipolis archive dc_161a0eebdada, sha256 04b4af44124c928bb35ff7666dbb45d334c12c5828ebd171ab1b871c5f21af97)

BibTeX

@misc{dc161a0eebdada,
  title = {A strongly compact cardinal yields a left and right coherent ring with $mathcalPGF(R)subsetneqmathcalGP(R)$ — arXiv:2608.17748},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.17748},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_161a0eebdada; sha256 04b4af44124c928bb35ff7666dbb45d334c12c5828ebd171ab1b871c5f21af97},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.17748. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

For a ring $R$, let $\mathcal{GP}(R)$, $\mathcal{GF}(R)$, and $\mathcal{PGF}(R)$ denote the classes of Gorenstein projective, Gorenstein flat, and projectively coresolved Gorenstein flat left $R$-modules, respectively. We isolate the local ultrafilter hypothesis $\textsf{LUH}$: the existence of a strongly compact cardinal implies $\textsf{LUH}$, while $\textsf{LUH}$ implies the existence of a measurable cardinal. Assuming $\textsf{LUH}$, we construct a left and right coherent ring $R$ and a strongly Gorenstein projective left $R$-module $G$ which is not Gorenstein flat; hence $\mathcal{PGF}(R)\subsetneq\mathcal{GP}(R)$.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-08-19 in math.LO).
Categorie arXiv: Rings and Algebras (math.RA) ; Commutative Algebra (math.AC); Logic (math.LO).
Pagina del lavoro: https://arxiv.org/abs/2608.17748 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-18T15:10:42.775Z dalla pagina https://arxiv.org/catchup/math.LO/2026-08-19?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).