{"paper":{"title":"Direct sums of representations as modules over their endomorphism rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Birge Huisgen-Zimmermann, Manuel Saor\\'in","submitted_at":"2014-07-09T06:12:13Z","abstract_excerpt":"This paper is devoted to the study of the endo-structure of infinite direct sums $\\bigoplus_{i \\in I} M_i$ of indecomposable modules $M_i$ over a ring $R$. It is centered on the following question: If $S = \\text{End}_R \\bigl( \\bigoplus_{i \\in I} M_i \\bigr)$, how much pressure, in terms of the $S$-structure of $\\bigoplus_{i \\in I} M_i$, is required to force the $M_i$ into finitely many isomorphism classes? In case the $M_i$ are endofinite (i.e., of finite length over their endomorphism rings), the number of isomorphism classes among the $M_i$ is finite if and only if $\\bigoplus_{i \\in I} M_i$ i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2364","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"}