Cale Bases in Algebraic Orders
Annales Mathématiques Blaise Pascal, Tome 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.

@article{AMBP_2003__10_1_117_0,
     author = {Picavet-L'Hermitte, Martine},
     title = {Cale Bases in Algebraic Orders},
     journal = {Annales Math\'ematiques Blaise Pascal},
     pages = {117--131},
     publisher = {Annales math\'ematiques Blaise Pascal},
     volume = {10},
     number = {1},
     year = {2003},
     doi = {10.5802/ambp.170},
     mrnumber = {1990013},
     zbl = {02068413},
     language = {en},
     url = {www.numdam.org/item/AMBP_2003__10_1_117_0/}
}
Picavet-L’Hermitte, Martine. Cale Bases in Algebraic Orders. Annales Mathématiques Blaise Pascal, Tome 10 (2003) no. 1, pp. 117-131. doi : 10.5802/ambp.170. http://www.numdam.org/item/AMBP_2003__10_1_117_0/

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