{"paper":{"title":"Generalized Artin-Schreier polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Fernando Szechtman, Natalio H. Guersenzvaig","submitted_at":"2013-06-17T19:45:07Z","abstract_excerpt":"Let $F$ be a field of prime characteristic $p$ containing $F_{p^n}$ as a subfield. We refer to $q(X)=X^{p^n}-X-a\\in F[X]$ as a generalized Artin-Schreier polynomial. Suppose that $q(X)$ is irreducible and let $C_{q(X)}$ be the companion matrix of $q(X)$. Then $ad\\, C_{q(X)}$ has such highly unusual properties that any $A\\in{\\mathfrak{ gl}}(m)$ such that $ad\\, A$ has like properties is shown to be similar to the companion matrix of an irreducible generalized Artin-Schreier polynomial.\n  We discuss close connections with the decomposition problem of the tensor product of indecomposable modules f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3967","kind":"arxiv","version":4},"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"}