{"paper":{"title":"Some finiteness results on monogenic orders in positive characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jason P. Bell, Khoa D. Nguyen","submitted_at":"2015-08-30T19:37:22Z","abstract_excerpt":"This work is motivated by the papers [EG85] and [Ngu15] in which the following two problems are solved. Let $\\mathcal{O}$ is a finitely generated $\\mathbb{Z}$-algebra that is an integrally closed domain of characteristic zero, consider the following problems:\n  (A) Fix $s$ that is integral over $\\mathcal{O}$, describe all $t$ such that $\\mathcal{O}[s]=\\mathcal{O}[t]$.\n  (B) Fix $s$ and $t$ that are integral over $\\mathcal{O}$, describe all pairs $(m,n)\\in\\mathbb{N}^2$ such that $\\mathcal{O}[s^m]=\\mathcal{O}[t^n]$.\n  In this paper, we solve these problems and provide a uniform bound for a certa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07624","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"}