{"paper":{"title":"Constructions cach\\'ees en alg\\`ebre abstraite. Dimension de Krull, Going Up, Going Down (revised version, 2008)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Henri Lombardi, Thierry Coquand","submitted_at":"2017-12-13T12:18:07Z","abstract_excerpt":"Nous rappelons des versions constructives de la th\\'eorie de la dimension de Krull dans les anneaux commutatifs et dans les treillis distributifs, dont les bases ont \\'et\\'e pos\\'ees par Joyal, Espan\\~ol et les deux auteurs. Nous montrons sur les exemples de la dimension des alg\\`ebres de pr\\'esentation finie, du Going Up, du Going Down \\ldots que cela nous permet de donner une version constructive de grands th\\'eor\\`emes classiques, et par cons\\'equent de r\\'ecup\\'erer un contenu calculatoire explicite lorsque ces th\\'eor\\`emes abstraits sont utilis\\'es pour d\\'emontrer l'existence d'objets c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.04728","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"}