대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제35권2호
  • /
  • Pages.481-486
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  • 2020
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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UNIT GROUPS OF QUOTIENTS OF NUMBER FIELDS

  • 투고 : 2019.07.19
  • 심사 : 2019.10.14
  • 발행 : 2020.04.30
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초록

Let K be a number field. Here we give an explicit description of the group (OK/I)* for most ideals I. In particular, we give a complete characterization of such group for those ideals I that are coprime to the different ideal 𝒟K.

키워드

참고문헌

  1. A. Harnchoowong and P. Ponrod, Unit groups of quotient rings of integers in some cubic fields, Commun. Korean Math. Soc. 32 (2017), no. 4, 789-803. https://doi.org/10.4134/CKMS.c160254
  2. G. Mantilla-Soler, Integral trace forms associated to cubic extensions, Algebra Number Theory 4 (2010), no. 6, 681-699. https://doi.org/10.2140/ant.2010.4.681
  3. J. Neukirch, Algebraic Number Theory, translated from the 1992 German original and with a note by Norbert Schappacher, Grundlehren der Mathematischen Wissenschaften, 322, Springer-Verlag, Berlin, 1999. https://doi.org/10.1007/978-3-662-03983-0
  4. A. Ranum, The group of classes of congruent quadratic integers with respect to a composite ideal modulus, Trans. Amer. Math. Soc. 11 (1910), no. 2, 172-198. https://doi.org/10.2307/1988676