{"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"}