{"paper":{"title":"Gorenstein $\\mathrm{FP}_n$-flat modules and weak global dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.RA","authors_text":"V\\'ictor Becerril","submitted_at":"2023-03-22T23:34:27Z","abstract_excerpt":"In this paper we characterize the relative Gorenstein weak global dimension of the generalized Gorenstein $\\mathrm{FP}_n$-flat $R$-modules and Projective Coresolved $\\mathrm{FP}_n$-flat $R$-modules recently studied by S. Estrada, A. Iacob, and M. A. P\\'erez. As application we prove that the weak global dimension that comes from the Gorenstein $\\mathrm{FP}_n$-flat modules is finite over a Gorenstein $n$-coherent ring and coincide with the flat dimension of the right $\\mathrm{FP}_n$-injective $R$-modules. This result extends the known for Gorenstein flat modules over Iwanaga-Gorenstein and Ding-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.12955","kind":"arxiv","version":3},"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/2303.12955/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"}