{"paper":{"title":"Group-theoretic and topological invariants of completely integrally closed Pr\\\"ufer domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Andreas Reinhart, Bruce Olberding, Olivier A. Heubo-Kwegna","submitted_at":"2015-12-10T16:34:03Z","abstract_excerpt":"We consider the lattice-ordered groups Inv$(R)$ and Div$(R)$ of invertible and divisorial fractional ideals of a completely integrally closed Pr\\\"ufer domain. We prove that Div$(R)$ is the completion of the group Inv$(R)$, and we show there is a faithfully flat extension $S$ of $R$ such that $S$ is a completely integrally closed B\\'ezout domain with Div$(R) \\cong $ Inv$(S)$. Among the class of completely integrally closed Pr\\\"ufer domains, we focus on the one-dimensional Pr\\\"ufer domains. This class includes Dedekind domains, the latter being the one-dimensional Pr\\\"ufer domains whose maximal "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03312","kind":"arxiv","version":2},"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"}