{"paper":{"title":"On cellular covers with free kernels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.AT","math.RA"],"primary_cat":"math.GR","authors_text":"Jos\\'e L. Rodr\\'iguez, Lutz Str\\\"ungmann","submitted_at":"2010-01-14T13:31:22Z","abstract_excerpt":"Recall that a homomorphism of $R$-modules $\\pi: G\\to H$ is called a {\\it cellular cover} over $H$ if $\\pi$ induces an isomorphism $\\pi_*: \\Hom_R(G,G)\\cong \\Hom_R(G,H),$ where $\\pi_*(\\varphi)= \\pi \\varphi$ for each $\\varphi \\in \\Hom_R(G,G)$ (where maps are acting on the left). In this paper we show that every cotorsion-free module $K$ of finite rank can be realized as the kernel of a cellular cover of some cotorsion-free module of rank 2. In particular, every free abelian group of any finite rank appears then as the kernel of a cellular cover of a cotorsion-free abelian group of rank 2. This si"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.2457","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"}