A class of number fields without odd rational prime index divisors and applications

Document Type : Research Paper

Authors

1 polydisciplinary faculty of Taza, Sidi Mohamed Ben Abdellah University Morocco

2 Department of mathematics, Faculty of sciences, Moulay Ismail University, Morocco

3 Polydisciplinary Faculty - Taza Sidi Mohamed Ben Abdellah University

Abstract

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.

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Journal of Algebra and Related Topics

Articles in Press, Accepted Manuscript
Available Online from 04 December 2024

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