{"paper":{"title":"Ultra LI-ideals in lattice implication algebras and MTL-algebras","license":"","headline":"","cross_cats":["math.GM"],"primary_cat":"math.LO","authors_text":"Keyun Qin, Wieslaw A. Dudek, Xiaohong Zhang","submitted_at":"2007-10-20T22:39:37Z","abstract_excerpt":"A mistake concerning the ultra \\textit{LI}-ideal of a lattice implication algebra is pointed out, and some new sufficient and necessary conditions for an \\textit{LI}-ideal to be an ultra \\textit{LI}-ideal are given. Moreover, the notion of an \\textit{LI}-ideal is extended to MTL-algebras, the notions of a (prime, ultra, obstinate, Boolean) \\textit{LI}-ideal and an \\textit{ILI}-ideal of an MTL-algebra are introduced, some important examples are given, and the following notions are proved to be equivalent in MTL-algebra: (1) prime proper \\textit{LI}-ideal and Boolean \\textit{LI}-ideal, (2) prime"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.3887","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"}