{"paper":{"title":"On principal congruences and the number of congruences of a lattice with more ideals than filters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Claudia Mure\\c{s}an, G\\'abor Cz\\'edli","submitted_at":"2017-11-17T04:15:54Z","abstract_excerpt":"Let $\\lambda$ and $\\kappa$ be cardinal numbers such that $\\kappa$ is infinite and either $2\\leq \\lambda\\leq \\kappa$, or $\\lambda=2^\\kappa$. We prove that there exists a lattice $L$ with exactly $\\lambda$ many congruences, $2^\\kappa$ many ideals, but only $\\kappa$ many filters. Furthermore, if $\\lambda\\geq 2$ is an integer of the form $2^m\\cdot 3^n$, then we can choose $L$ to be a modular lattice generating one of the minimal modular nondistributive congruence varieties described by Ralph Freese in 1976, and this $L$ is even relatively complemented for $\\lambda=2$. Related to some earlier resul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.06394","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"}