Cale Bases in Algebraic Orders
Let be a non-maximal order in a finite algebraic number field with integral closure . Although is not a unique factorization domain, we obtain a positive integer and a family (called a Cale basis) of primary irreducible elements of such that has a unique factorization into elements of for each coprime with the conductor of . Moreover, this property holds for each nonzero when the natural map is bijective. This last condition is actually equivalent to several properties linked...