{"paper":{"title":"Down-up algebras defined over a polynomial base ring $\\K[t_{1}, \\cdots, t_{n}]$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Xin Tang","submitted_at":"2014-03-26T00:21:06Z","abstract_excerpt":"In this paper, we study a class of down-up algebras $\\A$ defined over a polynomial base ring $\\K[t_{1}, \\cdots, t_{n}]$ and establish several analogous results. We first construct a $\\K-$basis for the algebra $\\A$. As a result, we prove that the Gelfand-Kirillov dimension of $\\A$ is $n+3$ and completely determine the center of $\\A$ when $char\\K=0$. Then, we prove that the algebra $\\A$ is a noetherian domain if and only if $\\beta\\neq 0$; and $\\A$ is Auslander-regular when $\\beta \\neq 0$. We also prove that the global dimension of $\\A$ is $n+3$; and the algebra $\\A$ is a prime ring except $\\alph"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6539","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"}