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Multiplicative Ideal Theory and Factorization Theory pp 323–352Cite as

Some Recent Results and Open Problems on Sets of Lengths of Krull Monoids with Finite Class Group

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 170))

Abstract

Some of the fundamental notions related to sets of lengths of Krull monoids with finite class group are discussed, and a survey of recent results is given. These include the elasticity and related notions, the set of distances , and the structure theorem for sets of lengths . Several open problems are mentioned.

Für Herrn Professor Halter-Koch zum siebzigsten Geburtstag

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Acknowledgments

The author is very grateful to the referee for many useful remarks and corrections. This work was supported by the ANR project Caesar, project number ANR-12-BS01-0011.

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Authors and Affiliations

  1. Université Paris 13, Sorbonne Paris Cité, LAGA, CNRS, UMR 7539, Université Paris 8, 99 Avenue Jean Baptiste Clément, 93430, Villetaneuse, France

    W. A. Schmid

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  1. W. A. Schmid
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Correspondence to W. A. Schmid .

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Editors and Affiliations

  1. Dept of Math & Stat, Sam Houston State University, Huntsville, Texas, USA

    Scott Chapman

  2. Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre, Rome, Italy

    Marco Fontana

  3. Institut für Mathematik und Wissenschaftliches Rechnen, Universität Graz, Graz, Austria

    Alfred Geroldinger

  4. Dept. Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico, USA

    Bruce Olberding

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Schmid, W.A. (2016). Some Recent Results and Open Problems on Sets of Lengths of Krull Monoids with Finite Class Group. In: Chapman, S., Fontana, M., Geroldinger, A., Olberding, B. (eds) Multiplicative Ideal Theory and Factorization Theory. Springer Proceedings in Mathematics & Statistics, vol 170. Springer, Cham. https://doi.org/10.1007/978-3-319-38855-7_14

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