Integral basis of pure prime degree number fields

Anuj Jakhar () and Neeraj Sangwan ()
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Anuj Jakhar: Indian Institute of Science Education and Research (IISER)
Neeraj Sangwan: Indian Institute of Science Education and Research (IISER)

Indian Journal of Pure and Applied Mathematics, 2019, vol. 50, issue 2, 309-314

Abstract: Abstract Let K = ℚ(θ) be an extension of the field ℚ of rational numbers where θ satisfies an irreducible polynomial xp − a of prime degree belonging to ℤ[x]. In this paper, we give explicilty an integral basis for K using only elementary algebraic number theory. Though an integral basis for such fields is already known (see [Trans. Amer. Math. Soc., 11 (1910), 388–392)], our description of integral basis is different and slightly simpler. We also give a short proof of the formula for discriminant of such fields.

Keywords: Rings of algebraic integers; integral basis and discriminant (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s13226-019-0326-7

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