On Monogenity of Certain Pure Number Fields Defined by x60 − m

Let θ be a root of a monic polynomial h(x) ∈ Z[x] of degree n ≥ 2. We say h(x) is monogenic if it is irreducible over Q and {1, θ, θ 2 , . . . , θ n−1 } is a basis for the ring Z K of integers of K = Q(θ). In this article, we study about the monogenity of number fields generated by a root of composition of two binomials. We characterise all the primes dividing the index of the subgroupm ≥ 1 and n ≥ 2. As an application, we provide a class of pairs of binomials f (x) = x n − a and g(x) = x m − b having the property that both f (x) and f (g(x)) are monogenic.

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A note on non-monogenity of number fields arised from sextic trinomials

Jakhar

Kaur

2022

Quaestiones Mathematicae

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On the index divisors and monogenity of number fields defined by x ⁵ + ax ³ + b

Fadil

2023

Quaestiones Mathematicae

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Monogenity and Power Integral Bases: Recent Developments

Gaál

2024

Axioms

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Monogenity is a classical area of algebraic number theory that continues to be actively researched. This paper collects the results obtained over the past few years in this area. Several of the listed results were presented at a series of online conferences titled “Monogenity and Power Integral Bases”. We also give a collection of the most important methods used in several of these papers. A list of open problems for further research is also given.

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On Monogenity of Certain Pure Number Fields Defined by x60 − m

Cited by 4 publications

References 23 publications

A note on non-monogenity of number fields arised from sextic trinomials

A note on non-monogenity of number fields arised from sextic trinomials

On the index divisors and monogenity of number fields defined by x ⁵ + ax ³ + b

Monogenity and Power Integral Bases: Recent Developments

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Resources

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On Monogenity of Certain Pure Number Fields Defined by x60 − m

Cited by 4 publications

References 23 publications

A note on non-monogenity of number fields arised from sextic trinomials

A note on non-monogenity of number fields arised from sextic trinomials

On the index divisors and monogenity of number fields defined by x 5 + ax 3 + b

Monogenity and Power Integral Bases: Recent Developments

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Product

Resources

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On the index divisors and monogenity of number fields defined by x ⁵ + ax ³ + b