{"paper":{"title":"Neat-Flat Modules","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.RA","authors_text":"Engin B\\\"uy\\\"uka\\c{s}{\\i}k, Y{\\i}lmaz Dur\\u{g}un","submitted_at":"2013-06-12T15:14:17Z","abstract_excerpt":"Let $R$ be a ring and $M$ be a right $R$-module. $M$ is called neat-flat if any short exact sequence of the form $0\\to K\\to N\\to M\\to 0$ is neat-exact i.e. any homomorphism from a simple right $R$-module $S$ to $M$ can be lifted to $N$. We prove that, a module is neat-flat if and only if it is simple-projective. Neat-flat right $R$-modules are projective if and only if $R$ is a right $\\sum$-$CS$ ring. Every finitely generated neat-flat right $R$-module is projective if and only if $R$ is a right $C$-ring and every finitely generated free right $R$-module is extending. Every cyclic neat-flat ri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.2860","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"}