Cale Bases in Algebraic Orders
Annales mathématiques Blaise Pascal, Volume 10 (2003) no. 1, pp. 117-131.

Let R be a non-maximal order in a finite algebraic number field with integral closure 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 xR coprime with the conductor of R. Moreover, this property holds for each nonzero xR when the natural map Spec(R ¯)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.

DOI: 10.5802/ambp.170
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, Volume 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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