My Math Forum Every quadratic field is contained in a cyclotomic field

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 June 5th, 2009, 06:25 PM #1 Senior Member   Joined: Nov 2007 Posts: 258 Thanks: 0 Every quadratic field is contained in a cyclotomic field This is a well known theorem. In perticular, the mth quadratic field, for m squarefree, is contained in the dth cyclotomic field, where $d= disc(R)$, the discriminant of the ring of algebraic integers in the mth quadratic field. Now my question is : is the dth cyclotomic field the cyclotomic field with least d containing the mth quadratic field?

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