On Sets of Irreducible Polynomials Closed by Composition

Autor:	Andrea Ferraguti, Giacomo Micheli, Reto Schnyder
Přispěvatelé:	Ferraguti, Andrea, Micheli, Giacomo, Schnyder, Reto
Jazyk:	angličtina
Rok vydání:	2017
Předmět:	Pure mathematics Finite field Semigroup 010102 general mathematics Generating set of a group Settore MAT/03 - Geometria 010103 numerical & computational mathematics 0101 mathematics 01 natural sciences Graph Monic polynomial Mathematics
Zdroj:	Arithmetic of Finite Fields ISBN: 9783319552262 WAIFI
Popis:	Let \(\mathcal {S}\) be a set of monic degree 2 polynomials over a finite field and let C be the compositional semigroup generated by \(\mathcal S\). In this paper we establish a necessary and sufficient condition for C to be consisting entirely of irreducible polynomials. The condition we deduce depends on the finite data encoded in a certain graph uniquely determined by the generating set \(\mathcal {S}\). Using this machinery we are able both to show examples of semigroups of irreducible polynomials generated by two degree 2 polynomials and to give some non-existence results for some of these sets in infinitely many prime fields satisfying certain arithmetic conditions.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::233ddefd7bf3f7a67f820a4f5a921615 http://hdl.handle.net/11379/561641 Zobrazit plný text záznamu