{"paper":{"title":"Zariski Topologies for Coprime and Second Submodules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.GN"],"primary_cat":"math.RA","authors_text":"Jawad Abuhlail","submitted_at":"2010-08-24T21:52:34Z","abstract_excerpt":"Let $M$ be a non-zero module over an associative (not necessarily commutative) ring. In this paper, we investigate the so-called \\emph{second} and \\emph{coprime} submodules of $M.$ Moreover, we topologize the spectrum $% \\mathrm{Spec}^{\\mathrm{s}}(M)$ of second submodules of $M$ and the spectrum $% \\mathrm{Spec}^{\\mathrm{c}}(M)$ of coprime submodules of $M,$ study several properties of these spaces and investigate their interplay with the algebraic properties of $M.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.4164","kind":"arxiv","version":2},"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"}