{"paper":{"title":"Pseudo MV-algebras and Lexicographic Product","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Anatolij Dvure\\v{c}enskij","submitted_at":"2014-06-09T20:07:27Z","abstract_excerpt":"We study algebraic conditions when a pseudo MV-algebra is an interval in the lexicographic product of an Abelian unital $\\ell$-group and an $\\ell$-group that is not necessary Abelian. We introduce $(H,u)$-perfect pseudo MV-algebras and strong $(H,u)$-perfect pseudo MV-algebras, the latter ones will have a representation by a lexicographic product. Fixing a unital $\\ell$-group $(H,u)$, the category of strong $(H,u)$-perfect pseudo MV-algebras is categorically equivalent to the category of $\\ell$-groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2339","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"}