Differences in sets of lengths of Krull monoids with finite class group

Wolfgang A. Schmid[1]

  • [1] Institut für Mathematik und Wissenschaftliches Rechnen Karl-Franzens-Universität Graz Heinrichstraße 36 8010 Graz, Austria

Journal de Théorie des Nombres de Bordeaux (2005)

  • Volume: 17, Issue: 1, page 323-345
  • ISSN: 1246-7405

Abstract

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Let H be a Krull monoid with finite class group where every class contains some prime divisor. It is known that every set of lengths is an almost arithmetical multiprogression. We investigate which integers occur as differences of these progressions. In particular, we obtain upper bounds for the size of these differences. Then, we apply these results to show that, apart from one known exception, two elementary p -groups have the same system of sets of lengths if and only if they are isomorphic.

How to cite

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Schmid, Wolfgang A.. "Differences in sets of lengths of Krull monoids with finite class group." Journal de Théorie des Nombres de Bordeaux 17.1 (2005): 323-345. <http://eudml.org/doc/249454>.

@article{Schmid2005,
abstract = {Let $H$ be a Krull monoid with finite class group where every class contains some prime divisor. It is known that every set of lengths is an almost arithmetical multiprogression. We investigate which integers occur as differences of these progressions. In particular, we obtain upper bounds for the size of these differences. Then, we apply these results to show that, apart from one known exception, two elementary $p$-groups have the same system of sets of lengths if and only if they are isomorphic.},
affiliation = {Institut für Mathematik und Wissenschaftliches Rechnen Karl-Franzens-Universität Graz Heinrichstraße 36 8010 Graz, Austria},
author = {Schmid, Wolfgang A.},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {lengths of factorizations; Krull monoids; finite Abelian groups; products of minimal elements; half-factorial sets},
language = {eng},
number = {1},
pages = {323-345},
publisher = {Université Bordeaux 1},
title = {Differences in sets of lengths of Krull monoids with finite class group},
url = {http://eudml.org/doc/249454},
volume = {17},
year = {2005},
}

TY - JOUR
AU - Schmid, Wolfgang A.
TI - Differences in sets of lengths of Krull monoids with finite class group
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2005
PB - Université Bordeaux 1
VL - 17
IS - 1
SP - 323
EP - 345
AB - Let $H$ be a Krull monoid with finite class group where every class contains some prime divisor. It is known that every set of lengths is an almost arithmetical multiprogression. We investigate which integers occur as differences of these progressions. In particular, we obtain upper bounds for the size of these differences. Then, we apply these results to show that, apart from one known exception, two elementary $p$-groups have the same system of sets of lengths if and only if they are isomorphic.
LA - eng
KW - lengths of factorizations; Krull monoids; finite Abelian groups; products of minimal elements; half-factorial sets
UR - http://eudml.org/doc/249454
ER -

References

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