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We say that $D$ is a $\\star $-power conductor domain ($\\star $-PCD) if for each pair $a,b\\in D\\backslash (0)$ and for each positive integer $n$ we have $Da^{n}\\cap Db^{n}=((Da\\cap Db)^{n})^{\\ast }.$ We study $\\star $-PCDs and characterize them as root closed domains satisfying $ ((a,b)^{n})^{-1}=(((a,b)^{-1})^{n})^{\\star }$ for all nonzero $a,b$ and all natural numbers $n\\geq 1$. From this it follows easily that Pr\\\"{u}fer domains are $d$-PCDs (where $d$ denotes the trivial star operation), and $v$ -domains (e.g., Krul"},"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":"1710.06521","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-10-17T22:50:37Z","cross_cats_sorted":[],"title_canon_sha256":"f6f8e0fced0689ea98c844e9b6bea1f08049124ce4ce323743bf2f979abef7bd","abstract_canon_sha256":"f7f8cbcc34dbb679dbe1993549343261aa7dbfc32412e61f4527ac93b5f7980b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:33.475397Z","signature_b64":"q5R5eVqkgnDiA+ElhiPdADHuFjqyoA5QFP8oDYYuT6zTuM2bFG6j0Ptozd4Hc6fy7XyplaOV29jAqW/PXulYBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f3916cc6152595520903201590a6409b18a24aac8d680c7260242238aa3bae2","last_reissued_at":"2026-05-18T00:32:33.474773Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:33.474773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On $\\star $-Power Conductor domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Daniel D. Anderson, Evan Houston, Muhammad Zafrullah","submitted_at":"2017-10-17T22:50:37Z","abstract_excerpt":"Let $D$ be an integral domain and $\\star $ a star operation defined on $D$. We say that $D$ is a $\\star $-power conductor domain ($\\star $-PCD) if for each pair $a,b\\in D\\backslash (0)$ and for each positive integer $n$ we have $Da^{n}\\cap Db^{n}=((Da\\cap Db)^{n})^{\\ast }.$ We study $\\star $-PCDs and characterize them as root closed domains satisfying $ ((a,b)^{n})^{-1}=(((a,b)^{-1})^{n})^{\\star }$ for all nonzero $a,b$ and all natural numbers $n\\geq 1$. From this it follows easily that Pr\\\"{u}fer domains are $d$-PCDs (where $d$ denotes the trivial star operation), and $v$ -domains (e.g., Krul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.06521","kind":"arxiv","version":1},"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":"1710.06521","created_at":"2026-05-18T00:32:33.474877+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.06521v1","created_at":"2026-05-18T00:32:33.474877+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.06521","created_at":"2026-05-18T00:32:33.474877+00:00"},{"alias_kind":"pith_short_12","alias_value":"B44RNTDBKJMV","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_16","alias_value":"B44RNTDBKJMVKIEQ","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_8","alias_value":"B44RNTDB","created_at":"2026-05-18T12:31:08.081275+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/B44RNTDBKJMVKIEQGIAVSCTEBG","json":"https://pith.science/pith/B44RNTDBKJMVKIEQGIAVSCTEBG.json","graph_json":"https://pith.science/api/pith-number/B44RNTDBKJMVKIEQGIAVSCTEBG/graph.json","events_json":"https://pith.science/api/pith-number/B44RNTDBKJMVKIEQGIAVSCTEBG/events.json","paper":"https://pith.science/paper/B44RNTDB"},"agent_actions":{"view_html":"https://pith.science/pith/B44RNTDBKJMVKIEQGIAVSCTEBG","download_json":"https://pith.science/pith/B44RNTDBKJMVKIEQGIAVSCTEBG.json","view_paper":"https://pith.science/paper/B44RNTDB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.06521&json=true","fetch_graph":"https://pith.science/api/pith-number/B44RNTDBKJMVKIEQGIAVSCTEBG/graph.json","fetch_events":"https://pith.science/api/pith-number/B44RNTDBKJMVKIEQGIAVSCTEBG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B44RNTDBKJMVKIEQGIAVSCTEBG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B44RNTDBKJMVKIEQGIAVSCTEBG/action/storage_attestation","attest_author":"https://pith.science/pith/B44RNTDBKJMVKIEQGIAVSCTEBG/action/author_attestation","sign_citation":"https://pith.science/pith/B44RNTDBKJMVKIEQGIAVSCTEBG/action/citation_signature","submit_replication":"https://pith.science/pith/B44RNTDBKJMVKIEQGIAVSCTEBG/action/replication_record"}},"created_at":"2026-05-18T00:32:33.474877+00:00","updated_at":"2026-05-18T00:32:33.474877+00:00"}