{"paper":{"title":"Algebraic Cuntz-Pimsner rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.RA","authors_text":"Eduard Ortega, Toke Meier Carlsen","submitted_at":"2008-10-17T21:31:14Z","abstract_excerpt":"From a system consisting of a right non-degenerate ring $R$, a pair of $R$-bimodules $Q$ and $P$ and an $R$-bimodule homomorphism $\\psi:P\\otimes Q\\longrightarrow R$ we construct a $\\Z$-graded ring $\\mathcal{T}_{(P,Q,\\psi)}$ called the Toeplitz ring and (for certain systems) a $\\Z$-graded quotient $\\mathcal{O}_{(P,Q,\\psi)}$ of $\\mathcal{T}_{(P,Q,\\psi)}$ called the Cuntz-Pimsner ring. These rings are the algebraic analogs of the Toeplitz $C^*$-algebra and the Cuntz-Pimsner $C^*$-algebra associated to a $C^*$-correspondence (also called a Hilbert bimodule).\n  This new construction generalizes for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.3254","kind":"arxiv","version":4},"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"}