Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
권호 표지

CIRCULAR UNITS OF ABELIAN FIELDS WITH A PRIME POWER CONDUCTOR

  • Kim, Jae Moon (Department of Mathematics Inha University) ;
  • Ryu, Ja do (Department of Mathematics Inha University)
  • Received : 2010.04.12
  • Accepted : 2010.06.07
  • Published : 2010.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

For an abelian extension K of ${\mathbb{Q}}$, let $C_W(K)$ be the group of Washington units of K, and $C_S(K)$ the group of Sinnott units of K. A lot of results about $C_S(K)$ have been found while very few is known about $C_W(K)$. This is mainly because elements in $C_S(K)$ are more explicitly defined than those in $C_W(K)$. The aim of this paper is to find a basis of $C_W(K)$ and use it to compare $C_W(K)$ and $C_S(K)$ when K is a subfield of ${\mathbb{Q}}({\zeta}_{p^e})$, where p is a prime.

Keywords

Acknowledgement

Supported by : Inha University

References

  1. C. Greither, Uber relativ-invariante Kreiseinheiten und Stickelberger- Elemente, Manuscripta Math. 80(1993), 27-43. https://doi.org/10.1007/BF03026535
  2. R. Kucera, On the Stickelberger ideal and circular units of some genus fields, Tatra Mt. Math. Publ. 20(2000), 93-104.
  3. W. Sinnott, On the Stickelberger ideal and the circular units of a cyclotomic field, Ann. of Math. (2) 108(1978), 107-134. https://doi.org/10.2307/1970932
  4. W. Sinnott, On the Stickelberger ideal and the circular units of an abelian field, Invent. Math. 62(1980), 181-234. https://doi.org/10.1007/BF01389158
  5. L. Washington, Introduction to Cyclotomic Fields, Graduate Texts in Math. 74, Springer-Verlag, New York/Berline, 1980.