{"paper":{"title":"A Factorization Algorithm for G-Algebras and Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC","math.OA"],"primary_cat":"math.RA","authors_text":"Albert Heinle, Viktor Levandovskyy","submitted_at":"2016-01-31T18:33:33Z","abstract_excerpt":"It has been recently discovered by Bell, Heinle and Levandovskyy that a large class of algebras, including the ubiquitous $G$-algebras, are finite factorization domains (FFD for short).\n  Utilizing this result, we contribute an algorithm to find all distinct factorizations of a given element $f \\in \\mathcal{G}$, where $\\mathcal{G}$ is any $G$-algebra, with minor assumptions on the underlying field.\n  Moreover, the property of being an FFD, in combination with the factorization algorithm, enables us to propose an analogous description of the factorized Gr\\\"obner basis algorithm for $G$-algebras"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.00296","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"}