Archiv der Mathematik

, Volume 84, Issue 2, pp 118–130

Formal power series with cyclically ordered exponents

Original Paper

DOI: 10.1007/s00013-004-1145-5

Cite this article as:
Giraudet, M., Kuhlmann, F.V. & Leloup, G. Arch. Math. (2005) 84: 118. doi:10.1007/s00013-004-1145-5


We define and study a notion of ring of formal power series with exponents in a cyclically ordered group. Such a ring is a quotient of various subrings of classical formal power series rings. It carries a two variable valuation function. In the particular case where the cyclically ordered group is actually totally ordered, our notion of formal power series is equivalent to the classical one in a language enriched with a predicate interpreted by the set of all monomials.

Mathematics Subject Classification (2000).

Primary 13A18 13A99 Secondary 06F99 

Copyright information

© Birkhäuser Verlag, Basel 2005

Authors and Affiliations

  1. Département de Mathématiques, Faculté des SciencesU.P.R.E.S.A. 7056 (Equipe de Logique, Paris VII)Le Mans CedexFrance
  2. 2.Mathematical Sciences GroupUniversity of SaskatchewanSaskatchewanCanada

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