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A class of number fields without odd rational prime index divisors | ||
| Journal of Algebra and Related Topics | ||
| دوره 13، شماره 2، اسفند 2025، صفحه 149-163 اصل مقاله (200.23 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2024.27125.1656 | ||
| نویسندگان | ||
| J. Didi1؛ M. Sahmoudi* 2؛ A. Chillali1 | ||
| 1Department of Mathematics, LSI Laboratory, University of Sidi Mohamed Ben Abdellah, Route d’Oujda, Taza, Morocco | ||
| 2Department of Mathematics, University of Moulay Ismail, Zitoune, Meknes, Morocco | ||
| چکیده | ||
| In this work, for every number field $K$ generated by a root of a monic irreducible trinomial $F(x) = x^{7} + a.x^{6} + b \in \mathbb{Z}[x]$, we show that no odd rational prime $p$ divides the index $i(K)$, and we give the necessary and sufficient conditions on a, b such that $2$ divides $i(K)$. Specifically, we provide adequate requirements for $K$ to be non-monogenic. Finally, several computational examples are used to illustrate our conclusions. | ||
| کلیدواژهها | ||
| Monogeneity؛ Newton polygon؛ Prime ideal factorization؛ Dedekind؛ Common index divisor؛ Theorem of Ore | ||
| مراجع | ||
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