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Integral basis of pure prime degree number fields

Author

Listed:
  • Anuj Jakhar

    (Indian Institute of Science Education and Research (IISER))

  • Neeraj Sangwan

    (Indian Institute of Science Education and Research (IISER))

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.

Suggested Citation

  • Anuj Jakhar & Neeraj Sangwan, 2019. "Integral basis of pure prime degree number fields," Indian Journal of Pure and Applied Mathematics, Springer, vol. 50(2), pages 309-314, June.
    • Handle: RePEc:spr:indpam:v:50:y:2019:i:2:d:10.1007_s13226-019-0326-7
    DOI: 10.1007/s13226-019-0326-7
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