Is the ring of all algebraic integers coherent? Here is the definition of a coherent ring.
Is the ring of all algebraic integers coherent?
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$\begingroup$
abstract-algebra
commutative-algebra
algebraic-number-theory
1 Answers
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Yes. In fact every finitely generated ideal is principal.
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0This is a little gross and there's probably an easier argument, but given a finitely generated ideal there is an ideal of an honest number field generated by the same generators; this ideal becomes principal after a finite extension (e.g. by capitulation of ideals in the Hilbert class field) and the generator of that new ideal is also a generator for your original ideal. – 2012-11-20