{"paper":{"title":"Quasi--bases for Modules over a Commutative Ring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Guang Shi","submitted_at":"2012-01-28T05:19:54Z","abstract_excerpt":"In this paper we present the definition of quasi-bases for modules over a ring that is commutative but not necessarily division and discuss properties that guarantee the existence of quasi-bases. Based on this result we further prove that every finitely generated module over $L^{0}(\\mathcal{F},K)$ has a quasi-basis, where $K$ is the scalar field of real numbers or complex numbers and $L^{0}(\\mathcal{F},K)$ is the algebra of equivalence classes of $K$--valued random variables defined on a probability space $(\\Omega,\\mathcal{F},P)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5925","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"}