{"paper":{"title":"Simplicity and Commutative Bases of Derivations in Polynomial and Power Series Rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Rene Baltazar","submitted_at":"2013-05-26T15:34:39Z","abstract_excerpt":"The first part of the paper will describe a recent result of K. Retert in (\\cite{Ret}) for $k[x_1,\\ldots,x_n]$ and $k[[x_1,\\ldots,x_n]]$. This result states that if $\\mathfrak{D}$ is a set of commute $k$-derivations of $k[x,y]$ such that both $\\partial_x \\in \\mathfrak{D}$ and the ring is $\\mathfrak{D}$-simple, then there is $d \\in \\mathfrak{D}$ such that $k[x,y]$ is $\\{\\partial_x,d\\}$-simple. As applications, we obtain relationships with known results of A. Nowicki on commutative bases of derivations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6035","kind":"arxiv","version":3},"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"}