{"paper":{"title":"$\\mathfrak{X}$-Gorenstein projective dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Xiaowei Xu, Zhibing Zhao","submitted_at":"2018-01-27T19:34:59Z","abstract_excerpt":"In this paper, we mainly investigate the $\\mathfrak{X}$-Gorenstein projective dimension of modules and the (left) $\\mathfrak{X}$-Gorenstein global dimension of rings. Some properties of $\\mathfrak{X}$-Gorenstein projective dimensions are obtained. Furthermore, we prove that the (left) $\\mathfrak{X}$-Gorenstein global dimension of ring $R$ is equal to the supremum of the set of $\\mathfrak{X}$-Gorenstein projective dimensions of all cyclic (left) $R$-modules. This result extends the well-known Auslander's theorem on the global dimension and its Gorenstein homological version."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09127","kind":"arxiv","version":2},"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"}