Pure Fields

István Gaál
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István Gaál: University of Debrecen, Institute of Mathematics

Chapter Chapter 12 in Diophantine Equations and Power Integral Bases, 2019, pp 197-205 from Springer

Abstract: Abstract In this section we give an overview on the monogenity properties of pure fields of type K = ℚ ( m n ) $$K={\mathbb Q}(\sqrt [n]{m})$$ for small values of n and square-free m. An explicit construction of the integral basis in K allows us to give conditions on the monogenity of K. We follow the presentation of Gaál and Remete (J Number Theory 173:129–146, 2017). We consider pure cubic, quartic, sextic, and octic fields in detail.

Date: 2019
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DOI: 10.1007/978-3-030-23865-0_12

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