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2002•Journal of the Korean Mathematical SocietyRequires access

CYCLOTOMIC UNITS AND DIVISIBILITY OF THE CLASS NUMBER OF FUNCTION FIELDS

Jae-Hyun Ahn, Hwanyup Jung

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Abstract

Let $textsc{k}$ ＝ $F_{q}$ (T) be a rational function field. Let $\ell$ be a prime number with ( $\ell$ , q-1) ＝ 1. Let K/ $textsc{k}$ be an elmentary abelian $\ell$ -extension which is contained in some cyclotomic function field. In this paper, we study the $\ell$ -divisibility of ideal class number $h_{K}$ of K by using cyclotomic units.s.s.

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Let $textsc{k}$ ＝ $F_{q}$ (T) be a rational function field. Let $\ell$ be a prime number with ( $\ell$ , q-1) ＝ 1. Let K/ $textsc{k}$ be an elmentary abelian $\ell$ -extension which is contained in some cyclotomic function field. In this paper, we study the $\ell$ -divisibility of ideal class number $h_{K}$ of K by using cyclotomic units.s.s.

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Available abstract

Let $textsc{k}$ ＝ $F_{q}$ (T) be a rational function field. Let $\ell$ be a prime number with ( $\ell$ , q-1) ＝ 1. Let K/ $textsc{k}$ be an elmentary abelian $\ell$ -extension which is contained in some cyclotomic function field. In this paper, we study the $\ell$ -divisibility of ideal class number $h_{K}$ of K by using cyclotomic units.s.s.

Key concepts: Divisibility rule, Mathematics, Function field, Abelian group, Cyclotomic field, Prime (order theory), Class number, Field (mathematics)

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