{"paper":{"title":"Triangular bases of integral closures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Hayden D. Stainsby","submitted_at":"2015-06-05T13:27:28Z","abstract_excerpt":"In this work, we consider the problem of computing triangular bases of integral closures of one-dimensional local rings.\n  Let $(K, v)$ be a discrete valued field with valuation ring $\\mathcal{O}$ and let $\\mathfrak{m}$ be the maximal ideal. We take $f \\in \\mathcal{O}[x]$, a monic irreducible polynomial of degree $n$ and consider the extension $L = K[x]/(f(x))$ as well as $\\mathcal{O}_{L}$ the integral closure of $\\mathcal{O}$ in $L$, which we suppose to be finitely generated as an $\\mathcal{O}$-module.\n  The algorithm $\\operatorname{MaxMin}$, presented in this paper, computes triangular bases"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01904","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"}