Article
Kummer Theory for Multiquadratic or Quartic Cyclic Number Fields
Authors
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Abstract
Let \( K \) be a number field which is multiquadratic or quartic cyclic.
We prove several results about the Kummer extensions of \( K \), namely
concerning the intersection between the Kummer extensions and the cyclotomic
extensions of \( K \). For \( G \) a finitely generated subgroup of
\( K^\times \), we consider the cyclotomic-Kummer extensions
\[
K(\zeta_{nt},\sqrt[t]{G})/K(\zeta_t)
\]
for all positive integers \( n \) and \( t \), and we describe an explicit
finite procedure to compute at once the degree of all these extensions.
Keywords
Kummer theory, Kummer extension, cyclotomic field, multiquadratic number.
Citation
Perissinotto, F. & Perucca, A. (2022). Kummer theory for multiquadratic or quartic cyclic number fields. Uniform Distribution Theory, 17(2), 176–206. https://doi.org/10.2478/udt-2022-0017
F. Perissinotto and A. Perucca, “Kummer theory for multiquadratic or quartic cyclic number fields,” Uniform Distribution Theory, vol. 17, no. 2, pp. 176–206, 2022, doi: 10.2478/udt-2022-0017.
Perissinotto F, Perucca A. Kummer theory for multiquadratic or quartic cyclic number fields. Uniform Distribution Theory. 2022;17(2):176–206. doi:10.2478/udt-2022-0017.
Perissinotto, F. and Perucca, A. (2022), ‘Kummer theory for multiquadratic or quartic cyclic number fields’, Uniform Distribution Theory, 17(2), pp. 176–206. Available at: https://doi.org/10.2478/udt-2022-0017.
Perissinotto, Flavio, and Antonella Perucca. “Kummer Theory for Multiquadratic or Quartic Cyclic Number Fields.” Uniform Distribution Theory, vol. 17, no. 2, 2022, pp. 176–206. https://doi.org/10.2478/udt-2022-0017.
Perissinotto, Flavio, and Antonella Perucca. “Kummer Theory for Multiquadratic or Quartic Cyclic Number Fields.” Uniform Distribution Theory 17, no. 2 (2022): 176–206. https://doi.org/10.2478/udt-2022-0017.
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Published by: Engineering Journals
