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A class of number fields without odd rational prime index divisors and applications | ||
| Journal of Algebra and Related Topics | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 14 آذر 1403 | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2024.27125.1656 | ||
| نویسندگان | ||
| J. Didi1؛ M. Sahmoudi* 2؛ A. Chillali3 | ||
| 1polydisciplinary faculty of Taza, Sidi Mohamed Ben Abdellah University Morocco | ||
| 2Department of mathematics, Faculty of sciences, Moulay Ismail University, Morocco | ||
| 3Polydisciplinary Faculty - Taza Sidi Mohamed Ben Abdellah University | ||
| 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 ∈ 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؛ Theorem of Ore | ||
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آمار تعداد مشاهده مقاله: 52 |
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