On Monogenicity of Relative Cubic-Power Pure Extensions

Sahmoudi, Mohammed; Soullami, Abderazak

doi:10.37418/amsj.9.9.40

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2021

2022

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Cited by 3 publications

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“…Parametrized families of monogenic polynomials have been given in [6,22]. In the Sections § § 3, 4 of the present article, we investigate the arithmetic of the cubic number field L = Q(θ) generated by a zero θ of a polynomial (1.1) P (X) = X 3 + aX − b, with a = σ • 3rb, sign σ ∈ {−1, +1}, and r, b ∈ N, which arises by specialization from the trinomials X p n + aX p s − b, p ∈ P, n > s ≥ 0, in [6].…”

Section: Introductionmentioning

confidence: 99%

Algebraic number fields generated by an infinite family of monogenic trinomials

Mayer¹,

Soullami²

2022

Preprint

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For an infinite family of monogenic trinomials Parithmetical invariants of the cubic number field L = Q(θ), generated by a zero θ of P (X), and of its Galois closure N = L( √ d L ) are determined. The conductor f of the cyclic cubic relative extension N/K, where K = Q( √ d L ) denotes the unique quadratic subfield of N , is proved to be of the form 3 e b with e ∈ {1, 2}, which admits statements concerning primitive ambiguous principal ideals, lattice minima, and independent units in L. The number m of non-isomorphic cubic fields L 1 , . . . , Lm sharing a common discriminant d L i = d L with L is determined.

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Section: Introductionmentioning

confidence: 99%