{"paper":{"title":"Gr\\\"obner-Shirshov bases for $L$-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Jiapeng Huang, L.A. Bokut, Yuqun Chen","submitted_at":"2010-05-02T02:20:47Z","abstract_excerpt":"In this paper, we firstly establish Composition-Diamond lemma for $\\Omega$-algebras. We give a Gr\\\"{o}bner-Shirshov basis of the free $L$-algebra as a quotient algebra of a free $\\Omega$-algebra, and then the normal form of the free $L$-algebra is obtained. We secondly establish Composition-Diamond lemma for $L$-algebras. As applications, we give Gr\\\"{o}bner-Shirshov bases of the free dialgebra and the free product of two $L$-algebras, and then we show four embedding theorems of $L$-algebras: 1) Every countably generated $L$-algebra  can be embedded into a two-generated $L$-algebra. 2) Every $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.0118","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"}