{"paper":{"title":"Contramodules over pro-perfect topological rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.CT","authors_text":"Leonid Positselski","submitted_at":"2018-07-27T15:11:17Z","abstract_excerpt":"For four wide classes of topological rings $\\mathfrak R$, we show that all flat left $\\mathfrak R$-contramodules have projective covers if and only if all flat left $\\mathfrak R$-contramodules are projective if and only if all left $\\mathfrak R$-contramodules have projective covers if and only if all descending chains of cyclic discrete right $\\mathfrak R$-modules terminate if and only if all the discrete quotient rings of $\\mathfrak R$ are left perfect. Three classes of topological rings for which this holds are the complete, separated topological associative rings with a base of neighborhood"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.10671","kind":"arxiv","version":6},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1807.10671/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}