On monogenity of certain pure number fields defined by xpr − m
| Autor: | Hamid Ben Yakkou, Lhoussain El Fadil |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Algebra and Number Theory
Irreducible polynomial Computer Science::Information Retrieval Astrophysics::Instrumentation and Methods for Astrophysics Root (chord) Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) Square-free integer Algebraic number field Combinatorics TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES Integer ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION ComputingMethodologies_DOCUMENTANDTEXTPROCESSING Computer Science::General Literature Prime integer ComputingMilieux_MISCELLANEOUS Monic polynomial Mathematics |
| Zdroj: | International Journal of Number Theory. 17:2235-2242 |
| ISSN: | 1793-7310 1793-0421 |
| Popis: | Let [Formula: see text] be a pure number field generated by a complex root [Formula: see text] of a monic irreducible polynomial [Formula: see text] where [Formula: see text] is a square free rational integer, [Formula: see text] is a rational prime integer, and [Formula: see text] is a positive integer. In this paper, we study the monogenity of [Formula: see text]. We prove that if [Formula: see text], then [Formula: see text] is monogenic. But if [Formula: see text] and [Formula: see text], then [Formula: see text] is not monogenic. Some illustrating examples are given. |
| Databáze: | OpenAIRE |
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