Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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KUCERA GROUP OF CIRCULAR UNITS IN FUNCTION FIELDS

  • Ahn, Jae-Hyun (DEPARTMENT OF MATHEMATICS CHUNGNAM NATIONAL UNIVERSITY) ;
  • Jung, Hwan-Yup (DEPARTMENT OF MATHEMATICS EDUCATION CHUNGBUK NATIONAL UNIVERSITY)
  • Published : 2007.05.31
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Abstract

Let $\mathbb{A}=\mathbb{F}_q$[T] be the polynomial ring over a finite field $\mathbb{F}_q$[T] and K=$\mathbb{F}_q$(T) its field of fractions. Let ${\ell}$ be a fixed prime divisor of q-1. Let J be a finite set of monic irreducible polynomials $P{\in}{\mathbb{A}}$ with deg $P{\equiv}0$ (mod ${\ell})$. In this paper we define the group $C_K$ of circular units in K=k$(\{\sqrt[{\ell}]P\;:\;P{\in}J\})$ in the sense of Kucera [4] and compute the index of $C_K$ in the full unit group $O^*_K$.

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References

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