{"paper":{"title":"Noncommutative Gr\\\"obner bases over rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Andr\\'e Mialebama Bouesso, Djiby Sow","submitted_at":"2012-08-12T17:09:06Z","abstract_excerpt":"In this work, it is proposed a method for computing Noncommutative Gr\\\"obner bases over a valuation n{\\oe}therian ring. We have generalized the fundamental theorem on normal forms over an arbitrary ring. The classical method of dynamical commutative Gr\\\"obner bases is generalized for Buchberger's algorithm over $R=\\mathcal{V}<x_1,...,x_m>$ a free associative algebra with non-commuting variables, where $\\mathcal{V}=\\mathbb{Z}/n\\mathbb{Z}$ or $\\mathcal{V}=\\mathbb{Z}$.\n  The process proposed, generalizes previous known technics for the computation of Commutative Gr\\\"obner bases over a valuation n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2442","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"}