{"paper":{"title":"Primitively generated Hopf orders in characteristic $p$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alan Koch","submitted_at":"2015-09-24T14:44:21Z","abstract_excerpt":"Let $R$ be a characteristic $p$ discrete valuation ring with field of fractions $K$. Let $H$ be a commutative, cocommutative $K$-Hopf algebra of $p$-power rank which is generated as a $K$-algebra by primitive elements. We construct all of the $R$-Hopf orders of $H$ in $K$; each Hopf order corresponds to a solution to a single matrix equation. For $R$ complete, we give explicit examples of Hopf orders in some rank $p^2$ $K$-Hopf algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07393","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"}