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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 $\\"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1903.09695","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-03-22T20:17:08Z","cross_cats_sorted":[],"title_canon_sha256":"9ee81518813a56d58c2c969870dbfb01e2cef947d7a4852263078426fc214fbb","abstract_canon_sha256":"9d77604a377ff558580bb46c3fc658d5cc6d2820579f4bee55499ca1369d855c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:35.767848Z","signature_b64":"OiPIDRlI7+bd9JXVDklIRRkdjvJy0IqWHU5zBsfAT82MHyqsE5gE7fu9adeFoaQG2UibKt4YW4zdEJ7qO1NwBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6d29939e400434c889d0579ab50c372bfbc936a13ac100268cc525e8c1846cf","last_reissued_at":"2026-05-17T23:50:35.767184Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:35.767184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $R$. 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