{"paper":{"title":"On the generalized distributive set of a finite nearfield","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Prudence Djagba","submitted_at":"2019-03-22T20:17:08Z","abstract_excerpt":"For any nearfield $(R,+, \\circ)$, denote by $D(R)$ the set of all distributive elements of $R$. Let $R$ be a finite Dickson nearfield that arises from Dickson pair $(q,n)$. For a given pair $(\\alpha, \\beta) \\in R^2$ we study the generalized distributive set $ D(\\alpha, \\beta)$ where $\"\\circ\"$ is the multiplication of the Dickson nearfield. We find that $ D(\\alpha, \\beta)$ is not in general a subfield of the finite field $\\mathbb{F}_{q^n}$. In contrast to the situation for $D(R)$, we also find that $D(\\alpha, \\beta)$ is not in general a subnearfield of $R$. We obtain sufficient conditions on $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.09695","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"}