The Conductor Ideal
نویسنده
چکیده
Let O be an order in the number field K. When O 6= OK , O is Noetherian and onedimensional, but is not integrally closed, so it has at least one nonzero prime ideal that’s not invertible and O doesn’t have unique factorization of ideals. That is, some nonzero ideal in O does not have a unique prime ideal factorization. We are going to define a special ideal in O, called the conductor, that is closely related to the noninvertible prime ideals in O. The nonzero ideals in O that are relatively prime to the conductor will be invertible and have unique factorization into prime ideals in O.
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