{"paper":{"title":"Explicit descriptions of the subfields $(NL)^{pi}$ and $(NL)^{pi}(NL)^{sep}$ of $NL$ and new explicit criteria for $NL = (NL)^{pi}(NL)^{sep}$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RA","authors_text":"V. V. Bavula","submitted_at":"2026-06-18T08:59:32Z","abstract_excerpt":"Let $L=K(\\theta)\\simeq K[x]/f(x)$ be a simple field extension in prime characteristic $p>0$, $L^{sep}$ and $L^{pi}$ be the maximal separable and purely inseparable subfields of $L$, respectively. Let $N/K$ be a purely inseparable field extension. For the field extensions $L/K$ and $NL/N$, the aim of the paper is to give explicit descriptions of the following subfields and their degrees in terms of the coefficients of the polynomial $f$ and two numerical field invariants $m_f$ and $m_{f,N}$: $L^{pi}$, $L^{pi}L^{sep}$, $(NL)^{pi}$ and $(NL)^{pi}(NL)^{sep}$. From these results, we derive new expl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.19962","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.19962/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}