{"paper":{"title":"On modules of integral elements over finitely generated domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Khoa D. Nguyen","submitted_at":"2014-12-09T06:38:43Z","abstract_excerpt":"This paper is motivated by the results and questions of Jason P. Bell and Kevin G. Hare in the paper \"On $\\mathbb{Z}$-modules of algebraic integers\" (Canad. J. Math. Vol. 61, 2009). Let $\\mathcal{O}$ be a finitely generated $\\mathbb{Z}$-algebra that is an integrally closed domain of characteristic zero. We investigate the following two problems:\n  (A) Fix $q$ and $r$ that are integral over $\\mathcal{O}$, describe all pairs $(m,n)\\in\\mathbb{N}^2$ such that $\\mathcal{O}[q^m]=\\mathcal{O}[r^n]$.\n  (B) Fix $r$ that is integral over $\\mathcal{O}$, describe all $q$ such that $\\mathcal{O}[q]=\\mathcal{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2868","kind":"arxiv","version":3},"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"}