{"paper":{"title":"On top local cohomology modules, Matlis duality and tensor products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"KH. Ahmadi-amoli, M. Eghbali, M.Y. Sadeghi","submitted_at":"2013-02-06T06:27:56Z","abstract_excerpt":"Let $\\mathfrak{a}$ be an ideal of a local ring $(R, \\mathfrak{m})$ with $c = \\mathrm{cd}(\\mathfrak{a},R)$ the cohomological dimension of $\\mathfrak{a}$ in $R$. In the case that $c=\\dim R$, we first give a bound for depth~$D(H^c_\\mathfrak{a}(R))$, where $c>2$ and $(R,\\mathfrak{m})$ is complete. Later, $H^c_\\mathfrak{a}(R) \\otimes_R H^c_\\mathfrak{a}(R)$, $D(H^c_\\mathfrak{a}(R)) \\otimes_R D(H^c_\\mathfrak{a}(R))$ and $H^c_\\mathfrak{a}(R) \\otimes_R D(H^c_\\mathfrak{a}(R))$ are examined. In the case $c=\\dim R-1$, the set Att$_R H^c_\\mathfrak{a}(R)$ is considered."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.1274","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"}