{"paper":{"title":"Non-monogenity in a family of octic fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Istv\\'an Ga\\'al, L\\'aszl\\'o Remete","submitted_at":"2018-09-27T08:42:43Z","abstract_excerpt":"Let $m$ be a square-free positive integer, $m\\equiv 2,3 \\; (\\bmod \\; 4)$. We show that the number field $K=Q(i,\\sqrt[4]{m})$ is non-monogene, that is it does not admit any power integral bases of type $\\{1,\\alpha,\\ldots,\\alpha^7\\}$. In this infinite parametric family of Galois octic fields we construct an integral basis and show non-monogenity using only congruence considerations.\n  Our method yields a new approach to consider monogenity or to prove non-monogenity in algebraic number fields. It is well applicable in parametric families of number fields. We calculate the index of elements as po"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10407","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"}