{"paper":{"title":"Chains of model structures arising from modules of finite Gorenstein dimension","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Nan Gao, Pu Zhang, Xue-Song Lu","submitted_at":"2024-03-08T11:45:33Z","abstract_excerpt":"For any integer $n\\ge 0$ and any ring $R$, \\ $(\\mathcal {PGF}_n, \\ \\mathcal P_n^\\perp \\cap \\mathcal {PGF}^{\\perp})$ proves to be a complete hereditary cotorsion pair in $R$-Mod, where $\\mathcal {PGF}$ is the class of PGF modules, introduced by J. \\v{S}aroch and J. \\v{S}\\'{t}ov\\'{i}\\v{c}ek, and \\ $\\mathcal {PGF}_n$ is the class of $R$-modules of PGF dimension $\\le n$. For any Artin algebra $R$, \\ $(\\mathcal {GP}_n, \\ \\mathcal P_n^\\perp \\cap \\mathcal {GP}^{\\perp})$ proves to be a complete and hereditary cotorsion pair in $R$-Mod, where $\\mathcal {GP}_n$ is the class of modules of Gorenstein proj"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.05232","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2403.05232/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}