{"paper":{"title":"The algebra of integro-differential operators on a polynomial algebra","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":"2009-12-03T20:20:12Z","abstract_excerpt":"We prove that the algebra $\\mI_n:=K\\langle x_1, ..., x_n, \\frac{\\der}{\\der x_1},...,\\frac{\\der}{\\der x_n}, \\int_1, ..., \\int_n\\rangle $ of integro-differential operators on a polynomial algebra is a prime, central, catenary, self-dual, non-Noetherian algebra of classical Krull dimension $n$ and of Gelfand-Kirillov dimension $2n$. Its weak homological dimension is $n$, and $n\\leq \\gldim (\\mI_n)\\leq 2n$. All the ideals of $\\mI_n$ are found explicitly, there are only finitely many of them ($\\leq 2^{2^n}$), they commute ($\\ga \\gb = \\gb\\ga$) and are idempotent ideals ($\\ga^2= \\ga$). The number of i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.0723","kind":"arxiv","version":2},"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"}