{"paper":{"title":"Quasi-Gorensteinness of extended Rees algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Youngsu Kim","submitted_at":"2013-09-16T16:08:53Z","abstract_excerpt":"Let $R$ be a Noetherian local ring and $I$ an $R$-ideal. It is well-known that if the associated graded ring $\\gr_I(R)$ is Cohen-Macaulay (Gorenstein), then so is $R$, but the converse is not true in general. In this paper we investigate the Cohen-Macaulayness and Gorensteinness of the associated graded ring $\\gr_I(R)$ under the hypothesis of the extended Rees algebra $R[It,t^{-1}]$ is quasi-Gorenstein or the associated graded ring $\\gr_I(R)$ is a domain."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4019","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"}