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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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1302.1274","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-02-06T06:27:56Z","cross_cats_sorted":[],"title_canon_sha256":"023f915d4f20a197ba919ba023551020ec4875f8c4fedaa1fc01915289411697","abstract_canon_sha256":"2f079e91c6d4e0e1736f28aa14aa9fa1ca01f8c4dc10c82343a659230ba8b7fc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:05.581875Z","signature_b64":"9xta7+Y9Jm3mAmLwTem/9Hh1OuYwOTpJsddEWvOAhE/a6kFxr6JDkpUDeMFHoVVLJ9TDwBeZhc8IatpIWLTaDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf2354278b871072130d373ff0253263e459e90c3749d27bdcb18f3763c4af7d","last_reissued_at":"2026-05-18T00:08:05.581497Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:05.581497Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1302.1274","created_at":"2026-05-18T00:08:05.581557+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.1274v2","created_at":"2026-05-18T00:08:05.581557+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.1274","created_at":"2026-05-18T00:08:05.581557+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z4RVIJ4LQ4IH","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z4RVIJ4LQ4IHEEYN","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z4RVIJ4L","created_at":"2026-05-18T12:28:09.283467+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Z4RVIJ4LQ4IHEEYNG477AJJSMP","json":"https://pith.science/pith/Z4RVIJ4LQ4IHEEYNG477AJJSMP.json","graph_json":"https://pith.science/api/pith-number/Z4RVIJ4LQ4IHEEYNG477AJJSMP/graph.json","events_json":"https://pith.science/api/pith-number/Z4RVIJ4LQ4IHEEYNG477AJJSMP/events.json","paper":"https://pith.science/paper/Z4RVIJ4L"},"agent_actions":{"view_html":"https://pith.science/pith/Z4RVIJ4LQ4IHEEYNG477AJJSMP","download_json":"https://pith.science/pith/Z4RVIJ4LQ4IHEEYNG477AJJSMP.json","view_paper":"https://pith.science/paper/Z4RVIJ4L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.1274&json=true","fetch_graph":"https://pith.science/api/pith-number/Z4RVIJ4LQ4IHEEYNG477AJJSMP/graph.json","fetch_events":"https://pith.science/api/pith-number/Z4RVIJ4LQ4IHEEYNG477AJJSMP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z4RVIJ4LQ4IHEEYNG477AJJSMP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z4RVIJ4LQ4IHEEYNG477AJJSMP/action/storage_attestation","attest_author":"https://pith.science/pith/Z4RVIJ4LQ4IHEEYNG477AJJSMP/action/author_attestation","sign_citation":"https://pith.science/pith/Z4RVIJ4LQ4IHEEYNG477AJJSMP/action/citation_signature","submit_replication":"https://pith.science/pith/Z4RVIJ4LQ4IHEEYNG477AJJSMP/action/replication_record"}},"created_at":"2026-05-18T00:08:05.581557+00:00","updated_at":"2026-05-18T00:08:05.581557+00:00"}