{"paper":{"title":"On the divisor-class group of monadic submonoids of rings of integer-valued polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Andreas Reinhart","submitted_at":"2016-04-12T21:35:19Z","abstract_excerpt":"Let $R$ be a factorial domain. In this work we investigate the connections between the arithmetic of ${\\rm Int}(R)$ (i.e., the ring of integer-valued polynomials over $R$) and its monadic submonoids (i.e., monoids of the form $\\{g\\in {\\rm Int}(R)\\mid g\\mid_{{\\rm Int}(R)} f^k$ for some $k\\in\\mathbb{N}_0\\}$ for some nonzero $f\\in {\\rm Int}(R)$). Since every monadic submonoid of ${\\rm Int}(R)$ is a Krull monoid it is possible to describe the arithmetic of these monoids in terms of their divisor-class group. We give an explicit description of these divisor-class groups in several situations and pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.03594","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"}