{"paper":{"title":"The global dimension of the algebras of polynomial integro-differential operators $\\mathbb{I}_n$ and the Jacobian algebras $\\mathbb{A}_n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RA","authors_text":"V. V. Bavula","submitted_at":"2017-05-11T19:05:24Z","abstract_excerpt":"The aim of the paper is to prove two conjectures that the (left and right) global dimension of the algebra of polynomial integro-differential operators $\\mathbb{I}_n$ and the Jacobian algebra $\\mathbb{A}_n$ is equal to $n$ (over a field of characteristic zero). An analogue of Hilbert's Syzygy Theorem is proven for them. The algebras $\\mathbb{I}_n$ and $\\mathbb{A}_n$ are neither left nor right Noetherian. Furthermore, they contain infinite direct sums of nonzero left/right ideals and are not domains. It is proven that the global dimension of all prime factor algebras of the algebras $\\mathbb{I}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05227","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"}