{"paper":{"title":"A special class of congruences on $\\kappa$-frames","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Graham Manuell","submitted_at":"2017-05-19T16:51:30Z","abstract_excerpt":"Madden has shown that in contrast to the situation with frames, the smallest dense quotient of a $\\kappa$-frame need not be Boolean. We characterise these so-called d-reduced $\\kappa$-frames as those which may be embedded as a generating sub-$\\kappa$-frame of a Boolean frame. We introduce the notion of the closure of a $\\kappa$-frame congruence and call a congruence clear if it is the largest congruence with a given closure. These ideas are used to prove $\\kappa$-frame analogues of known results concerning Boolean frame quotients. In particular, we show that d-reduced $\\kappa$-frames are preci"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.07085","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"}