{"paper":{"title":"Stability of Gorenstein flat categories with respect to a semidualizing module","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.RA","authors_text":"Jianlong Chen, Zhenxing Di, Zhongkui Liu","submitted_at":"2012-10-29T00:35:20Z","abstract_excerpt":"In this paper, we first introduce $\\mathcal {W}_F$-Gorenstein modules to establish the following Foxby equivalence:\n$\\xymatrix@C=80pt{\\mathcal {G}(\\mathcal {F})\\cap \\mathcal {A}_C(R) \\ar@<0.5ex>[r]^{C\\otimes_R-} & \\mathcal {G}(\\mathcal {W}_F) \\ar@<0.5ex>[l]^{\\textrm{Hom}_R(C,-)}} $\nwhere $\\mathcal {G}(\\mathcal {F})$, $\\mathcal {A}_C(R) $ and $\\mathcal {G}(\\mathcal {W}_F)$ denote the class of Gorenstein flat modules, the Auslander class and the class of $\\mathcal {W}_F$-Gorenstein modules respectively. Then, we investigate two-degree $\\mathcal {W}_F$-Gorenstein modules. An $R$-module $M$ is sai"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.7529","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}