{"paper":{"title":"On classes of C3 and D3 modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Abyzov Adel Nailevich, Tran Hoai Ngoc Nhan, Truong Cong Quynh","submitted_at":"2016-09-13T21:07:29Z","abstract_excerpt":"The aim of this paper is to study the notions of $\\mathcal{A}$-C3 and $\\mathcal{A}$-D3 modules for some class $\\mathcal{A}$ of right modules. Several characterizations of these modules are provided and used to describe some well-known classes of rings and modules. For example, a regular right $R$-module $F$ is a $V$-module if and only if every $F$-cyclic module $M$ is an $\\mathcal{A}$-C3 module where $\\mathcal{A}$ is the class of all simple submodules of $M$. Moreover, let $R$ be a right artinian ring and $\\mathcal{A}$, a class of right $R$-modules with local endomorphisms, containing all simp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04052","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"}