# Cale Bases in Algebraic Orders

Martine Picavet-L’Hermitte^{[1]}

- [1] Laboratoire de Mathématiques Pures Université Blaise Pascal Les Cézeaux 63177 AUBIERE CEDEX FRANCE

Annales mathématiques Blaise Pascal (2003)

- Volume: 10, Issue: 1, page 117-131
- ISSN: 1259-1734

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topPicavet-L’Hermitte, Martine. "Cale Bases in Algebraic Orders." Annales mathématiques Blaise Pascal 10.1 (2003): 117-131. <http://eudml.org/doc/10480>.

@article{Picavet2003,

abstract = {Let $R$ be a non-maximal order in a finite algebraic number field with integral closure $\overline\{R\}$. Although $R$ is not a unique factorization domain, we obtain a positive integer $N$ and a family $\{\mathcal\{Q\}\}$ (called a Cale basis) of primary irreducible elements of $R$ such that $x^N$ has a unique factorization into elements of $\{\mathcal\{Q\}\}$ for each $x\in R$ coprime with the conductor of $R$. Moreover, this property holds for each nonzero $x\in R$ when the natural map $\mathrm\{Spec\}(\overline\{R\})\rightarrow \mathrm\{Spec\}(R)$ is bijective. This last condition is actually equivalent to several properties linked to almost divisibility properties like inside factorial domains, almost Bézout domains, almost GCD domains.},

affiliation = {Laboratoire de Mathématiques Pures Université Blaise Pascal Les Cézeaux 63177 AUBIERE CEDEX FRANCE},

author = {Picavet-L’Hermitte, Martine},

journal = {Annales mathématiques Blaise Pascal},

keywords = {orders; Cale bases; factorization},

language = {eng},

month = {1},

number = {1},

pages = {117-131},

publisher = {Annales mathématiques Blaise Pascal},

title = {Cale Bases in Algebraic Orders},

url = {http://eudml.org/doc/10480},

volume = {10},

year = {2003},

}

TY - JOUR

AU - Picavet-L’Hermitte, Martine

TI - Cale Bases in Algebraic Orders

JO - Annales mathématiques Blaise Pascal

DA - 2003/1//

PB - Annales mathématiques Blaise Pascal

VL - 10

IS - 1

SP - 117

EP - 131

AB - Let $R$ be a non-maximal order in a finite algebraic number field with integral closure $\overline{R}$. Although $R$ is not a unique factorization domain, we obtain a positive integer $N$ and a family ${\mathcal{Q}}$ (called a Cale basis) of primary irreducible elements of $R$ such that $x^N$ has a unique factorization into elements of ${\mathcal{Q}}$ for each $x\in R$ coprime with the conductor of $R$. Moreover, this property holds for each nonzero $x\in R$ when the natural map $\mathrm{Spec}(\overline{R})\rightarrow \mathrm{Spec}(R)$ is bijective. This last condition is actually equivalent to several properties linked to almost divisibility properties like inside factorial domains, almost Bézout domains, almost GCD domains.

LA - eng

KW - orders; Cale bases; factorization

UR - http://eudml.org/doc/10480

ER -

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