{"paper":{"title":"For which additive submonoids $M$ of nonnegative rationals is $F[X;M]$ AP?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Hamid Kulosman, Ryan Gipson","submitted_at":"2018-05-25T21:45:48Z","abstract_excerpt":"We characterize the submonoids $M$ of the additive monoid $\\Q_+$ of nonnegative rational numbers for which the irreducible and the prime elements in the monoid domain $F[X;M]$ coincide. We present a diagram of implications between some types of submonoids of $\\Q_+$, with a precise position of the monoids $M$ with this property."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10373","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"}