{"paper":{"title":"On injective and Gorenstein injective dimensions of local cohomology modules","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Hossein Zakeri, Majid Rahro Zargar","submitted_at":"2012-04-11T09:59:08Z","abstract_excerpt":"Let $(R,\\fm)$ be a commutative Noetherian local ring and let $M$ be an $R$-module which is a relative Cohen-Macaulay with respect to a proper ideal $\\fa$ of $R$ and set $n:=\\h_{M}\\fa$. We prove that $\\ind M<\\infty$ if and only if $\\ind\\H^{n}_\\fa(M)<\\infty$ and that $\\ind\\H^{n}_\\fa(M)=\\ind M-n$. We also prove that if $R$ has a dualizing complex and $\\Gid_{R} M<\\infty$, then $\\Gid_{R}\\H^{n}_\\fa(M)<\\infty$ and $\\Gid_{R}\\H^{n}_\\fa(M)=\\Gid_{R} M-n$. Moreover if $R$ and $M$ are Cohen-Macaulay, then it is proved that $\\Gid_{R} M<\\infty$ whenever $\\Gid_{R}\\H^{n}_\\fa(M)<\\infty$. Next, for a finitely ge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2394","kind":"arxiv","version":5},"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"}