{"paper":{"title":"The Dickson Subcategory Splitting Conjecture for Pseudocompact Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA","math.RT"],"primary_cat":"math.CT","authors_text":"Blas Torrecillas-Jover, Constantin Nastasescu, M. C. Iovanov","submitted_at":"2011-09-20T05:44:45Z","abstract_excerpt":"Let $A$ be a pseudocompact (or profinite) algebra, so $A=C^*$ where $C$ is a coalgebra. We show that the if the semiartinian part (the \"Dickson\" part) of every $A$-module $M$ splits off in $M$, then $A$ is semiartinian, also giving a positive answer in the case of algebras arising as dual of coalgebras (pseudocompact algebras), to a well known conjecture of Faith."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4210","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"}