Maqola

On cubic equations over p-adic fields

Farrukh MukhamedovDepartment of Computational and Theoretical Sciences, Faculty of Sciences, International Islamic University Malaysia, P. O. Box 141, Kuantan, 25710 Pahang, MalaysiaB. A. OmirovInstitute of Mathematics, National University of Uzbekistan, Tashkent 100125, UzbekistanMansoor SaburovDepartment of Computational and Theoretical Sciences, Faculty of Sciences, International Islamic University Malaysia, P. O. Box 141, Kuantan, 25710 Pahang, Malaysia

International Journal of Number Theoryjournal2014en

ABI

Annotatsiya

We provide a solvability criterion for a cubic equation in domains [Formula: see text]. We show that, in principal, the Cardano method is not always applicable for such equations. Moreover, the numbers of solutions of the cubic equation in domains [Formula: see text] are provided. Since 𝔽 p is a subgroup of ℚ p , we generalize Serre's and Sun's results concerning with cubic equations over the finite field 𝔽 p . Finally, all cubic equations, for which the Cardano method could be applied, are described and the p-adic Cardano formula is provided for those cubic equations.

Mavzular

advanced mathematical theories Algebraic Geometry and Number Theory

Identifikatorlar

DOI: 10.1142/s1793042114500201

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