{"paper":{"title":"A new Composition-Diamond lemma for dialgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Guangliang Zhang, Yuqun Chen","submitted_at":"2017-02-01T04:14:50Z","abstract_excerpt":"Let $Di\\langle X\\rangle$ be the free dialgebra over a field generated by a set $X$. Let $S$ be a monic subset of $Di\\langle X\\rangle$. A Composition-Diamond lemma for dialgebras is firstly established by Bokut, Chen and Liu in 2010 \\cite{Di} which claims that if (i) $S$ is a Gr\\\"{o}bner-Shirshov basis in $Di\\langle X\\rangle$, then (ii) the set of $S$-irreducible words is a linear basis of the quotient dialgebra $Di\\langle X \\mid S \\rangle$, but not conversely. Such a lemma based on a fixed ordering on normal diwords of $Di\\langle X\\rangle$ and special definition of composition trivial modulo $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.00119","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"}