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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  3. S. T. Chapman and W. W. Smith. Factorization in Dedekind domains with finite class group. Israel J. Math., 71(1):65–95, 1990. Zbl0717.13014MR1074505
  4. S. T. Chapman, W. A. Schmid, and W. W. Smith. On minimum distances in Krull monoids with infinite class group. Bull. Lond. Math. Soc., 40(4):613–618, 2008. Zbl1198.20049MR2441133
  5. G. Freiman and A. Geroldinger. An addition theorem and its arithmetical application. J. Number Theory, 85(1):59–73, 2000. Zbl1019.11002MR1800301
  6. W. Gao and A. Geroldinger. Systems of sets of lengths. II. Abh. Math. Sem. Univ. Hamburg, 70:31–49, 2000. Zbl1036.11054MR1809532
  7. A. Geroldinger. Über nicht-eindeutige Zerlegungen in irreduzible Elemente. Math. Z., 197(4):505–529, 1988. Zbl0618.12002MR932683
  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 / n / n via the system of sets of lengths. Abh. Math. Sem. Hamburg, 79:25–35, 2009. Zbl1191.20069MR2541341

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