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Recently, in Theorem 1.2 of \\cite{Nu1}, it is proved that in a Noetherian regular local ring $S$ and for a fixed ideal $J\\subset S$, associated primes of local cohomology module $H^i_J(S)$ for $i\\geq 0$ is finite, if it does not contain $p$. In this paper, we study how the property $\\textit{\\textbf{P}}$ (as menti"},"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":"1512.05686","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-12-17T17:38:17Z","cross_cats_sorted":[],"title_canon_sha256":"97d0255ae91f3c1c9daba1f0f7d3b2a28e06fbf806a23b992c66f499ea5447c6","abstract_canon_sha256":"3e0e758c0bd190758bb2432cc53a8cb7c0efe098bc120f17e0bb08cc1c670885"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:09.493293Z","signature_b64":"COLkmJYbZdtTQQ0VTRJiSEz1KRxDcVhpfTIGy2ruRjcjbtgiBp8e/VybsQwj+fnYE042FMl4nmUnVO+Tt6FWBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f79c085e073c5e9a75f093cd08eed82e360c28f4a1c8cf29f5261470d2c03710","last_reissued_at":"2026-05-18T01:24:09.492722Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:09.492722Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Note on Associated Primes and Bockstein Homomorphisms of Local Cohomology Modules for Ramified Regular Local Rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Rajsekhar Bhattacharyya","submitted_at":"2015-12-17T17:38:17Z","abstract_excerpt":"For a Noetherian regular ring $S$ and for a fixed ideal $J\\subset S$, assume that the associated primes of local cohomology module $H^i_J(S)$ does not contain $p$ for some $i\\geq 0$, and we call this as a property $\\textit{\\textbf{P}}^{i,p}_{J,S}$ or $\\textit{\\textbf{P}}$ for brevity. Recently, in Theorem 1.2 of \\cite{Nu1}, it is proved that in a Noetherian regular local ring $S$ and for a fixed ideal $J\\subset S$, associated primes of local cohomology module $H^i_J(S)$ for $i\\geq 0$ is finite, if it does not contain $p$. 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