### Abstract

Let K be an abelian number field of conductor f and p a prime. Sinnott defined circular units C_{K}^{s} of K using the norm maps from the cyclotomic units of the nth cyclotomic fields for all n and Washington defined circular units C_{K}^{w} of K to be the Galois invariant of the cyclotomic units of the f th cyclotomic field. In this note, we investigate a question raised by Kolster in [5] of whether the projective limits of circular units of Sinnott and Washington over the cyclotomic Z _{p}-extension of K are equal. Belliard [2] and Kučera [6] found independently some counter examples to this question. The purpose of this note is to find some conditions on the ground field K under which Kolster's question has an affirmative answer.

Original language | English |
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Pages (from-to) | 117-123 |

Number of pages | 7 |

Journal | Manuscripta Mathematica |

Volume | 115 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2004 Sep |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)