{"paper":{"title":"Gr\\\"obner-Shirshov Bases for Commutative Algebras with Multiple Operators and Free Commutative Rota-Baxter Algebras","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Jianjun Qiu","submitted_at":"2013-01-18T09:51:51Z","abstract_excerpt":"In this paper, the Composition-Diamond lemma for commutative algebras with multiple operators is established. As applications, the Gr\\\"obner-Shirshov bases and linear bases of free commutative Rota-Baxter algebra, free commutative $\\lambda$-differential algebra and free commutative $\\lambda$-differential Rota-Baxter algebra are given, respectively. Consequently, these three free algebras are constructed directly by commutative $\\Omega$-words."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5018","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"}