{"paper":{"title":"$t$-local domains and valuation domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.RA"],"primary_cat":"math.AC","authors_text":"Marco Fontana, Muhammad Zafrullah","submitted_at":"2018-12-10T10:13:01Z","abstract_excerpt":"In a valuation domain $(V,M)$ every nonzero finitely generated ideal $J$ is principal and so, in particular, $J=J^t$, hence the maximal ideal $M$ is a $t$-ideal. Therefore, the $t$-local domains (i.e., the local domains, with maximal ideal being a $t$-ideal) are \"cousins\" of valuation domains, but, as we will see in detail, not so close. Indeed, for instance, a localization of a $t$-local domain is not necessarily $t$-local, but of course a localization of a valuation domain is a valuation domain.\n  So it is natural to ask under what conditions is a $t$-local domain a valuation domain? The mai"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.03713","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"}