# 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

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topPhilipp, 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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