{"paper":{"title":"Factorizations in rational monogenic semidomains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Anna Deng, Felix Gotti, Jason Zeng","submitted_at":"2026-07-11T07:47:01Z","abstract_excerpt":"For $\\alpha \\in \\mathbb{C}$, the monogenic semidomain generated by $\\alpha$ is the smallest subsemiring $S_\\alpha$ of the complex field $\\mathbb{C}$ containing $\\alpha$. We initiate a systematic study of the arithmetic and factorizations of the monogenic semidomains $S_q$ generated by rational parameters $q$. After some preliminaries, we introduce and investigate the monoid of technical fractions $T_q$, which is a divisor-closed submonoid of the multiplicative monoid of $S_q$ that encodes a significant amount of arithmetic information about $S_q$. We then study several fundamental factorizatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.10178","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.10178/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}