Title: Two classes of number fields with a non-principal Euclidean ideal,
Abstract: This paper introduces two classes of totally real quartic number fields, one
of biquadratic extensions and one of cyclic extensions, each of which has a
non-principal Euclidean ideal. It generalizes techniques of Graves used to
prove that the number field $\mathbb{Q}(\sqrt{2},\sqrt{35})$ has a
non-principal Euclidean ideal.