Cale Bases in Algebraic Orders

Martine Picavet-L’Hermitte

doi:10.5802/ambp.170

Martine Picavet-L’Hermitte ¹

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

Annales mathématiques Blaise Pascal, Tome 10 (2003) no. 1, pp. 117-131.

Résumé

Let $R$ be a non-maximal order in a finite algebraic number field with integral closure $\bar{R}$ . Although $R$ is not a unique factorization domain, we obtain a positive integer $N$ and a family $𝒬$ (called a Cale basis) of primary irreducible elements of $R$ such that $x^{N}$ has a unique factorization into elements of $𝒬$ 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 $Spec (\bar{R}) \to Spec (R)$ 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.

MR Zbl

DOI : 10.5802/ambp.170

Affiliations des auteurs :

Martine Picavet-L’Hermitte ¹

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

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Martine Picavet-L’Hermitte. Cale Bases in Algebraic Orders. Annales mathématiques Blaise Pascal, Tome 10 (2003) no. 1, pp. 117-131. doi : 10.5802/ambp.170. https://ambp.centre-mersenne.org/articles/10.5802/ambp.170/

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