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Groups in the class semigroups of valuation domains

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Abstract

It is shown that the isomorphy classes of the ideals of a valuation domain form a Clifford semigroup, and the structure of this semigroup is investigated. The group constituents of this Clifford semigroup are exactly the quotients of totally ordered complete abelian groups, modulo dense subgroups. A characterization of these groups is obtained, and some realization results are proved when the skeleton of the totally ordered group is given.

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Authors and Affiliations

  1. Dipartimento di Matematica Pura e Applicata, Università di Padova, Via Belzoni 7, 35131, Padova, Italy

    S. Bazzoni & L. Salce

Authors
  1. S. Bazzoni
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  2. L. Salce
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Correspondence to S. Bazzoni.

Additional information

The authors are members of GNSAGA of CNR. This research was supported by Ministero dell'Università e della Ricerca Scientifica e Tecnologica, Italy.

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Bazzoni, S., Salce, L. Groups in the class semigroups of valuation domains. Israel J. Math. 95, 135–155 (1996). https://doi.org/10.1007/BF02761037

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  • DOI: https://doi.org/10.1007/BF02761037

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