Arithmetic of non-principal orders in algebraic number fields

Andreas Philipp[1]

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

Actes des rencontres du CIRM (2010)

  • Volume: 2, Issue: 2, page 99-102
  • ISSN: 2105-0597

Abstract

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Let R be an order in an algebraic number field. If R is a principal order, then many explicit results on its arithmetic are available. Among others, R is half-factorial if and only if the class group of R has at most two elements. Much less is known for non-principal orders. Using a new semigroup theoretical approach, we study half-factoriality and further arithmetical properties for non-principal orders in algebraic number fields.

How to cite

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Philipp, Andreas. "Arithmetic of non-principal orders in algebraic number fields." Actes des rencontres du CIRM 2.2 (2010): 99-102. <http://eudml.org/doc/196273>.

@article{Philipp2010,
abstract = {Let $R$ be an order in an algebraic number field. If $R$ is a principal order, then many explicit results on its arithmetic are available. Among others, $R$ is half-factorial if and only if the class group of $R$ has at most two elements. Much less is known for non-principal orders. Using a new semigroup theoretical approach, we study half-factoriality and further arithmetical properties for non-principal orders in algebraic number fields.},
affiliation = {Institut für Mathematik und Wissenschaftliches Rechnen Karl-Franzens-Universität Graz Heinrichstraße 36 8010 Graz, Austria},
author = {Philipp, Andreas},
journal = {Actes des rencontres du CIRM},
keywords = {non-unique factorizations; half-factoriality; non-principal orders; algebraic number fields},
language = {eng},
number = {2},
pages = {99-102},
publisher = {CIRM},
title = {Arithmetic of non-principal orders in algebraic number fields},
url = {http://eudml.org/doc/196273},
volume = {2},
year = {2010},
}

TY - JOUR
AU - Philipp, Andreas
TI - Arithmetic of non-principal orders in algebraic number fields
JO - Actes des rencontres du CIRM
PY - 2010
PB - CIRM
VL - 2
IS - 2
SP - 99
EP - 102
AB - Let $R$ be an order in an algebraic number field. If $R$ is a principal order, then many explicit results on its arithmetic are available. Among others, $R$ is half-factorial if and only if the class group of $R$ has at most two elements. Much less is known for non-principal orders. Using a new semigroup theoretical approach, we study half-factoriality and further arithmetical properties for non-principal orders in algebraic number fields.
LA - eng
KW - non-unique factorizations; half-factoriality; non-principal orders; algebraic number fields
UR - http://eudml.org/doc/196273
ER -

References

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