Towards a more precise understanding of sets of lengths

Wolfgang A. Schmid[1]

  • [1] CMLS, École polytechnique, 91128 Palaiseau cedex, France

Actes des rencontres du CIRM (2010)

  • Volume: 2, Issue: 2, page 103-105
  • ISSN: 2105-0597

Abstract

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This short survey, based on the content of a talk with the same title, summarizes some classical and recent results on the set of differences of an abelian group. We put a certain emphasize on ongoing joint work of A. Plagne and the author. We also briefly review the relevance of this notion in Non-unique Factorization Theory, in particular towards the subject mentioned in the title.

How to cite

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Schmid, Wolfgang A.. "Towards a more precise understanding of sets of lengths." Actes des rencontres du CIRM 2.2 (2010): 103-105. <http://eudml.org/doc/196272>.

@article{Schmid2010,
abstract = {This short survey, based on the content of a talk with the same title, summarizes some classical and recent results on the set of differences of an abelian group. We put a certain emphasize on ongoing joint work of A. Plagne and the author. We also briefly review the relevance of this notion in Non-unique Factorization Theory, in particular towards the subject mentioned in the title.},
affiliation = {CMLS, École polytechnique, 91128 Palaiseau cedex, France},
author = {Schmid, Wolfgang A.},
journal = {Actes des rencontres du CIRM},
keywords = {Dedekind domain; factorization; Krull monoid; set of differences; set of lengths; zero-sum sequence},
language = {eng},
number = {2},
pages = {103-105},
publisher = {CIRM},
title = {Towards a more precise understanding of sets of lengths},
url = {http://eudml.org/doc/196272},
volume = {2},
year = {2010},
}

TY - JOUR
AU - Schmid, Wolfgang A.
TI - Towards a more precise understanding of sets of lengths
JO - Actes des rencontres du CIRM
PY - 2010
PB - CIRM
VL - 2
IS - 2
SP - 103
EP - 105
AB - This short survey, based on the content of a talk with the same title, summarizes some classical and recent results on the set of differences of an abelian group. We put a certain emphasize on ongoing joint work of A. Plagne and the author. We also briefly review the relevance of this notion in Non-unique Factorization Theory, in particular towards the subject mentioned in the title.
LA - eng
KW - Dedekind domain; factorization; Krull monoid; set of differences; set of lengths; zero-sum sequence
UR - http://eudml.org/doc/196272
ER -

References

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  8. A. Geroldinger and F. Halter-Koch. Non-unique factorizations. Algebraic, Combinatorial and Analytic Theory. Chapman & Hall/CRC, 2006. Zbl1113.11002MR2194494
  9. A. Geroldinger and Y. ould Hamidoune. Zero-sumfree sequences in cyclic groups and some arithmetical application. J. Théor. Nombres Bordeaux, 14(1):221–239, 2002. Zbl1018.11011MR1925999
  10. A. Plagne and W. A. Schmid. On congruence half-factorial Dedekind domains with cyclic class group. Manuscript in progress. 
  11. W. A. Schmid. Arithmetical characterization of class groups of the form via the system of sets of lengths. Abh. Math. Sem. Hamburg, 79:25–35, 2009. Zbl1191.20069MR2541341

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