{"paper":{"title":"Some remarks on infinitesimals in MV-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Eduardo J. Dubuc, Jorge Zilber","submitted_at":"2016-02-16T21:03:50Z","abstract_excerpt":"Replacing $\\{0\\}$ by the whole ideal of infinitesimals yields a weaker notion of \\emph{archimedean element} that we call \\emph{quasiarchimedean}. It is known that semisimple MV-algebras with compact maximal spectrum (in the co-Zarisky topology) are exactly the hyperarchimedean algebras. We characterise all the algebras with compact maximal spectrum as being \\emph{quasihyperarchimedean} \\mbox{MV-algebras,} which in a sense are non semisimple hyperarchimedean algebras. We develop some basic facts in the theory of MV-algebras along the lines of algebraic geometry, where infinitesimals play the ro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05204","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"}