Discriminant and Integral basis of sextic fields defined by x⁶+ax+b

2020/11/29 by Kaur, Sumandeep, Khanduja, Sudesh Kaur
#11R04 #11R29 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2011.14348

Abstract

Let K=\mathbb Q(θ) be an algebraic number field with θ a root of an irreducible trinomial f(x)=x⁶+ax+b belonging to ℤ[x]. In this paper, for each prime number p we compute the highest power of p dividing the discriminant of K in terms of the prime powers dividing a,~b and discriminant of f(x). An explicit p-integral basis of K is also given for each prime p and a method is described to obtain an integral basis of K from these p-integral bases which is illustrated with examples.

Related

• Discriminant and integral basis of pure nonic fields
• Calculating generators of power integral bases in sextic fields with a quadratic subfield: the general case
• DISCRIMINANT and integral basis OF ℚ(√[12]a)
• An elementary computation of the Galois groups of symmetric sextic trinomials
• Monogenic sextic trinomials x⁶+Ax³+B and their Galois groups